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Open Access Article
1 - 𝐶𝑣-injectivity of S-acts over monoids
Masoome Hezarjaribi Dastaki Hamid RasouliIn 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 mo MoreIn 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. Manuscript profile
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