JOURNAL OF ALGEBRAIC SYSTEMS
Year:2020 | Volume:8 | Issue:1|Papers Count:13

In this paper we define φ-Connes module amenability of a dual Banach algebra A where φ is a bounded wk∗-module homomorphism from A to A. We are mainly concerned with the study of φ-module normal virtual diagonals. We show that if S is a weakly cancellative inverse semigroup with subsemigroup E of idempotents, χ is a bounded wk∗-module homomorphism from l1(S) to l1(S) and l1(S) as a Banach module over l1(E) is χ-Connes module amenable, then it has a χ-module normal virtual diagonal. In the case χ =id, the converse holds

Let R be a multiplicative hyperring. In this paper, we introduce and study the concept of n-absorbing hyperideal which is a generalization of prime hyperideal. A proper hyperideal I of R is called an n-absorbing hyperideal of R if whenever α 1o. . . oα n+1⊆ I for α 1, . . ., α n+1∈ R, then there are n of the α , is whose product is in I.

Let R be a commutative ring with identity and M be a unitary R-module. An R-module M is called a multiplication module if for every submodule N of M there exists an ideal I of R such that N=IM. It is shown that over a Noetherian domain R with dim(R)≤ 1, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of R. Moreover, we give a characterization of finitely generated multiplication modules.

In this work, we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules. Let R be a commutative ring with identity. We say that a non-zero submodule N of an R-module M is a \emph{classical 2-absorbing secondary submodule} of M if whenever a, b∈ R, K is a submodule of M and abN⊆ K, then aN⊆ K or bN⊆ K or ab∈ AnnR(N)− − − − − − − − √ . This can be regarded as a dual notion of the 2-absorbing primary submodule.

A topological group H is called ω-narrow if for every neighbourhood V of it’ s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also let G be a topological space and the operation and inversion mapping are continuous, then G is called a topological generalized group. If {e(x) | x ∈ G} is countable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ω-narrow topological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topological generalized groups are introduced and studied.

In this paper, we investigate po-purity using fi nitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly fi nitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right congruence on S. Finally, the relationships between regular injectivity and absolute po-purity are considered.

In this work, we investigate admitting center map on multiplicative metric space and establish some fixed point theorems for such maps. We modify the Banach contraction principle and the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some useful theorems. Our results on multiplicative metric space improve and modify some fixed point theorems in the literature.

Let R be a commutative ring with identity and let M be an R-module. We define the primary spectrum of M, denoted by PS(M), to be the set of all primary submodules Q of M such that (radQ: M)=(Q: M)− − − − − − √ . In this paper, we topologize PS(M) with a topology having the Zariski topology on the prime spectrum Spec(M) as a subspace topology. We investigate compactness and irreducibility of this topological space and provide some conditions under which PS(M) is a spectral space.

To a simple graph G=(V, E), we correspond a simple graph G△ , □ whose vertex set is {{x, y}: x, y∈ V} and two vertices {x, y}, {z, w}∈ G△ , □ are adjacent if and only if {x, z}, {x, w}, {y, z}, {y, w}∈ V∪ E. The graph G△ , □ is called the (△ , □ )-edge graph of the graph G. In this paper, our ultimate goal is to provide a link between the connectedness of G and G△ , □ .

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥ 0, under the ring extension R⊂ R[X] (resp. R⊂ R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, in [11], holds in R[[X]], then it will holds in R.

Let G be a finite group, in this paper using the order and largest element order of G we show that every fi nite group with the same order and largest element order as G 2 (q), where q  11 is necessarily isomorphic to the group G 2 (q).

The tensor product is the fundamental ingredient for extending one-dimensional techniques of filtering and compression in signal preprocessing to higher dimensions. Woven frames play a crucial role in signal preprocessing and distributed data processing. Motivated by these facts, we have investigated the tensor product of woven frames and presented some of their properties. Besides, we have studied some effects of operators on woven frames in the tensor products of Hilbert spaces.