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Information Journal Paper

Title

𝐶 𝑣-injectivity of S-acts over monoids

Pages

  147-159

Abstract

 In this paper, the notion of C_v-injectivity of Monoid acts is studied. The behavior of C_v-injectivity with respect to products, coproducts and direct sums is investigated. We characterize Monoids over which all acts are C_v-injective and show that any act over such Monoids is vitally injective. The class of acts satisfying C_v-injectivity is determined. By means of the notion of C_v-injectivity, we find conditions over which any projective act is injective. Also, it is shown that on a left reversible Monoid, any C_v-injective act with zero is C-injective. We prove that if any C_v-injective act on Monoid S is vital injective, then Monoid S is left leversible. Using the concept of vitally injective envelope, a class of C_v-injective acts is obtained. Moreover, we consider the notion of M_v-injectivity as a generalization of CC-injectivity and study when the factor act of an M_v-injective act is M_v-injective. As a result, we show that any factor of a principally weakly vital injective act is principally weakly vital injective.

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    • Cite

    APA: Copy

    Hezarjaribi Dastaki, Masoome, & Rasouli, Hamid. (2021). 𝐶 𝑣-injectivity of S-acts over monoids. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(28 ), 147-159. SID. https://sid.ir/paper/952281/en

    Vancouver: Copy

    Hezarjaribi Dastaki Masoome, Rasouli Hamid. 𝐶 𝑣-injectivity of S-acts over monoids. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;6(28 ):147-159. Available from: https://sid.ir/paper/952281/en

    IEEE: Copy

    Masoome Hezarjaribi Dastaki, and Hamid Rasouli, “𝐶 𝑣-injectivity of S-acts over monoids,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 28 , pp. 147–159, 2021, [Online]. Available: https://sid.ir/paper/952281/en

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