𝐶𝑣-injectivity of S-acts over monoids

Subject Areas : Statistics

Masoome  Hezarjaribi Dastaki ¹ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran)
Hamid  Rasouli ² (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran)

Received: 2019-08-15 Accepted : 2019-11-09 Published : 2021-02-19

Keywords: S-سیستم, تکواره, زیر سیستم وایتال, C_v-انژکتیو,

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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