Let M AND P be RIGHT R-MODULEs. A SUBMODULE K of an R-MODULE M is called P-dense if for each m Î M; (K: m) is a P-faithful RIGHT ideal of R: PR is nonsingular if AND only if, for each R-MODULE M; every essential SUBMODULE of M is a P-dense SUBMODULE. For any R-MODULE M, we obtain P-rational extention of M AND equivalent condition in order that M is equal with its P-rational extention is found. An R-MODULE P is called RIGHT KASCH if every simple R-MODULE can be embedded in P: Finally, we given some equivalent conditions for an R-MODULE P to be RIGHT KASCH.

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The dual notion of a nil MODULE AND the square SUBMODULE of a MODULE over a commutative ring are de, ned. Moreover, besides other results, some properties of these new concepts are investigated.

Let M be a MODULE over a commutative ring R. We continue our study of strongly annihilating SUBMODULE graph SAG(M) introduced in [11]. In addition to providing the more properties of this graph, we introduce the subgraph SAG∗ (M) of SAG(M) AND compare the properties of SAG∗ (M) with SAG(M) AND AG(M) (the annihilating SUBMODULE graph of M introduced in [4]).

Introduction: Arbitration has a contractual nature AND is subject to the sovereignty of the will of the parties, but in some cases, the legislator imposed the referral of claims to arbitration on the will of the parties AND caused the contractual nature of the arbitration clause to disappear or be limited. By doing this, he has placed the arbitration outside the will of the parties. This issue causes some moral conflicts in the discussion of compulsory arbitration. Therefore, this research has been done with the purpose of examining the position of compulsory arbitration in Iran's legal system AND the ethical challenges in it with a descriptive-analytical approach. Material AND Methods: The research was a review method, in order to achieve the goal of the research, in addition to electronic education books AND virtual education in this field, articles related to the research keywords from 2004 to 2022 from the databases of Civilica, Magiran, Sid, Researchgate, Science direct, was reviewed Conclusion: Based on the findings of the research, it can be concluded that compulsory arbitration in Iran has ethical challenges in the field of implementation AND interpretation, the most important of which is the issue of the RIGHT to action AND judicial justice. In the context of ambiguities in mANDatory arbitration, even if the method of arbitration becomes ambiguous, the arbitrator has the duty to find out the will of the legislator with the principles AND rules of interpretation, which creates a moral conflict for the arbitrator.

ABSTRACT RIGHT to the city is one of the most important citizenship RIGHTs that can be reduced for women under different circumstances. In this mixed research, with in-depth AND semi-structured interviews, a conceptual model has been presented to explain the causal, contextual AND interventional conditions effectively reducing women's RIGHT to the city. Then, with the structural equation modeling, the causal conditions affecting the RIGHT to the city have been investigated. Family, ethnicity, AND physical AND mental conditions were the most important background conditions that 32 women living in Ahvaz pointed to in order to influence the RIGHT to the city. Also, the participants considered politics AND government institutions, law, AND spatial policies as the most important intervention in the women's RIGHT to the city. City security, favorable actions with the city space, space-positive gender performance, AND social welfare were among the most important causal conditions that the participants mentioned in increasing women's RIGHT to the city. Causal modeling showed that the most influential reason for reducing women's RIGHT to the city of Ahvaz is urban space security, followed by urban policies AND designs. By multiplying the causal path, it is 0.84, followed by urban planning AND design with a coefficient of 0.79. Governmental AND executive institutions should pay more attention to women's RIGHT to the city through the establishment of better laws, the design of suitable spaces with individual differences, especially gender, AND, of course, with an emphasis on women. The creation of safer places in the city for women while increasing the livability of the city for citizens improves women's RIGHTs in urban spaces Extended abstract Introduction The RIGHT to the city is a universal RIGHT consisting of several instances. Since the RIGHT to the city enables the city inhabitants to access AND enjoy the urban life benefits freely, it is tantamount to the RIGHT to freedom. The RIGHT to the city, the RIGHT to freedom of building AND rebuilding cities, is one of the most valuable AND, at the same time, the most neglected human RIGHTs. Among governments, NGOs (Non-Governmental Organizations) AND political activists in all scales, the RIGHT to the city is often conceived in a legal meaning. In this sense, the RIGHT to city includes a set of distinct RIGHTs to urban resources AND services, shelter, public space, clean water, AND education that must be available to all, regardless of social or economic status, the bearers of such RIGHTs are urban dwellers AND their guarantor is the government. This legal conception of the RIGHT to the city emphasizes universal AND individual RIGHTs in the global liberal institutional order. The ultimate normative purpose of a legal RIGHT to the city is that the government legally encodes AND enforces the set of RIGHTs constituting the RIGHT to the city. Justice AND equality have been considered since long ago; however, injustice AND discrimination are still visible in cities. Among all kinds of injustices AND discrimination, gender equality has been a subject marginalized in all ages. In Iran, the need for urban spaces for women in accordance with the civil needs of citizens in daily life is felt. In Iran, factors such as various types of urban violence AND insecurity, which generally make women victims, have reduced the possibility AND desire for their presence AND participation in public. Because the spatial, temporal, official AND unofficial divisions in the city have caused some spaces to remain far from the reach of women. In this research, we intend to deal with the most important factors that cause women not to enjoy one of their most essential human RIGHTs, which is the RIGHT to the city.   Methodology This research, which is practical in terms of purpose, has been done with a confirmatory mixed method; first, it tried to present the most important contextual, interventional, AND causal factors effective in reducing the RIGHT to the city of women in the form of a conceptual model by the approach of grounded theory, AND then confirming the defined causal structure with the help of structural equations modeling. The population in this research is Iranian women who are exposed to gender injustice AND do not have the RIGHT to a desirable city. Research participants have a deep experience of undermining their RIGHT to the city AND are interested in sharing it AND cooperating with the researcher. Sampling was purposefully selected from women with the least amount of the RIGHT to the city. The qualitative sample of the research was 32 people, AND the quantitative sample was 420 people. Due to the mixed nature of the research AND the use of the data-driven theory approach AND, afterwards, structural equations to collect the data, the interview was used in the qualitative phase AND questionnaires in the quantitative phase. The interviews were done in-depth, face-to-face AND semi-structured. The open-ended interview questions were conducted in a calm environment without the presence of a third person, AND the time of the interviews varied according to the conditions of the interviewee. The questionnaire used in the research has ascertained an instrument that evaluates the contextual AND causal components AND factors related to the RIGHT to the city in the form of self-declaration items. The data obtained from the interview, after being implemented in the form of text, were analyzed AND classified with the help of directed content analysis. In order to investigate the causal structure of the RIGHT to the city, structural equation modeling would have been helpful. Analyzes were performed with the help of LISREL 8.8. To estimate the causal path coefficients, the iterated maximum likelihood method was used AND the overall fit of the causal structure model of women’s RIGHT to the city was carried out by Chi-square statistic. AND, of course, the most important fit indexes of the model, such as absolute fit indexes, incremental fit indexes AND Parsimonious Normed Fit Indexes (PNFI).   Results AND discussion Directed content analysis helped us to identify the factors reducing the RIGHT to the city AND its subclasses of Iranian women. Conditions affecting women's RIGHT to the city are divided into underlying conditions, causal conditions, AND intervening conditions. The most critical underlying conditions were family, age, ethnicity, AND physical AND mental characteristics. At the same time, environment security, urban actions, social welfare, AND space gender functions constituted the essential intervening conditions, AND politics, governmental institutions, law, AND city spatial policies included the most important intervening conditions. Causal modeling also showed that the factors influencing women's RIGHT to the city are the most influential to the least influential in the form of (1) security of the city environment, (2) urban policy-making, (3) gender function of space, AND (4) interaction with the city. Security is one of the most important AND influential factors that can decrease or increase the RIGHT to the city for women.   Conclusion The RIGHT to the city, which is considered one of the most fundamental RIGHTs of citizens, is trampled or reaches its lowest level due to underlying reasons such as the gender of individuals or their families. In this case, women are more vulnerable than the men. In such a way, causal conditions such as environmental security or urban actions AND, of course, welfare have made this gender difference in the use of city space deeper AND more complicated. Meanwhile, the role of governments AND sovereignty in legislation AND policies should not be neglected to reduce the RIGHT to city for women. Our explicit suggestion is for governmental institutions AND executive agencies to pay more attention to women’s RIGHT to the city through the establishment of better laws, the design of more suitable spaces in the city, the design of urban spaces away from any gender discrimination only with the view of equal access for all AND the creation of safer places for the women living in Ahvaz.   Funding There is no funding support.   Authors’ Contribution All of the authors approved the content of the manuscript AND agreed on all aspects of the work.   Conflict of Interest Authors declared no conflict of interest.   Acknowledgments We are grateful to all the scientific.

Let MR be a non-zero MODULE AND F: s [MR]´s [MR]®Mod-Z a bifunctor. The F-reversibility of M is defined by F(X, Y)=0ÞF (Y, X)=0 for all non-zero X, Y in s [MR]. Hom (resp. Rej)-reversibility of M is characterized in different ways. Among other things, it is shown that RR (RR) is Hom-reversible if AND only if R= Åni=1 Ri such that each Ri is a perfect ring with a unique simple MODULE (up to isomorphism). In particular, for a duo ring, the concepts of perfectness AND Hom-reversibility coincide.

Let R be a commutative ring with identity AND let M be a unitary R -MODULE. Then we study the properties of prime AND semiprime SUBMODULEs AND consider the connection between some semiprime SUBMODULEs of M AND the quotient MODULE M s (a subset S of a ring R is said to be multiplicatively closed if whenever s, s´ belong to S, then their product ss´ also belongs to S). Also we prove some results, which have been already proved when the MODULEs are free, concerning the prime SUBMODULEs of any arbitrary R MODULE.

An $R$-MODULE $M$ is called torsion-free, if $rx=0$ for $r\in R$ AND $x\in M$ implies that $r=0$ or $x=0$. In this paper, we introduce the notions semi torsion-free MODULEs AND quasi torsion-free MODULEs. We show that a SUBMODULE $N$ of an $R$-MODULE $M$ is a $P$-primary SUBMODULE if AND only if $\dfrac{R}{P}$-MODULE $\dfrac{M}{N}$ is semi torsion-free. Also we define a new radical in free MODULEs AND find some characterizations of it. We prove that for $P$-SUBMODULE $N$ of a free $R$-MODULE $F$ which $\sqrt N \subsetneqq F$, we have for any $r \in R$ AND $m \in F$, $rm \in N$ implies $r \in \sqrt P$ or $m \in \sqrt N$ if AND only if $\dfrac{R}{P}$-MODULE $\dfrac{F}{N}$ is quasi torsion free.