Document Type: Original Manuscript


1 Lamerd Higher Education Center, Lamerd, Iran.

2 Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 71454, Shiraz, Iran.

3 Department of Mathematics, Jahrom University, P.O. Box 74135-11, Jahrom, Iran.



This paper is a continuation of recent researches concerning generalization of
injectivity of acts over moniods, namely, C-injectivity and InD-injectivity. We introduce new
kinds of injectivity, such as, LC-injectivity and CQ-injectivity. Classi cations 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.