Title of article :
SOME CLASSIFICATIONS OF MONOIDS BY VARIOUS NOTIONS OF INJECTIVITY OF ACTS
Author/Authors :
Roueentan, M. Lamerd Higher Education Center, Lamerd, Iran , Ershad, M. Department of Mathematics - College of Sciences - Shiraz University, Shiraz, Iran , Naghipoor, M. A. Department of Mathematics - Jahrom University, Jahrom, Iran.
Abstract :
This paper is a continuation of recent researches concerning generalization of
in jectivity of acts over mo nio ds , namely, C - injectivity and In D-injectivity. We introduce new kinds of in jectivity, such as, LC-in jectivity and CQ-in jectivity. Classications of monoids by properties of these kinds of injective acts are presented. It is proved that a monoid S is completely (cyclic) injective if and only if it is completely quasi (CQ-) injective. Some results on quasi-injective acts are proved. Also new characterizations for right hereditary monoids and right PP-monoids are given.
Keywords :
Locally cyclic (weakly) , C- injective act , injective act Indecomposable (weakly) injective act
Journal title :
Journal of Algebraic Systems
