# Pseudo PQ-injective systems over monoids

### Abstract

The purpose of this paper is to introduce a new kind of generalization of principally quasi injective S-systems over monoids (PQ-injective), (and hence generalized quasi injective), namely pseudo principally quasi injective S-systems over monoids. Several properties of this kind of generalization are discussed. Some of these properties are analogous to that notion of pseudo principally quasi injective class of general modules. Sufficient conditions are given for pseudo principally quasi injective S-systems to beprincipally quasi-injective and pseudo quasi principally injective S-systems. Characterizations of pseudo principally quasi injective S-systems are considered.### Downloads

### References

A . M .Lopez , Jr. and J. K. Luedeman, (1979) , Quasi-injective S-systems and their S-endomorphism semi group, CzechoslovakMath .J., 29(1), pp.97-104.

A.M.Lopez, Jr. and J.K.Luedeman , (1976) , The Bicommutator of the injective hull of a non- singular semigroup, Semigroup Forum, 12 , pp.71-77.

C.V. Hinkle and Jr. , (1974) ,The extended centralizer of an S-set , Pacific journal of mathematics , Vol.53, No.1, pp 163-170.

K.Jupil , (2008), PI-S-systems , J. of Chungcheong Math. Soc., 21 , no.4,pp.591-599.

M . Kilp , U . Knauer and A .V . Mikhalev , (2000) , Monoids acts and categories . Walter de Gruyter , Berlin , New York.

M.S. Abbas and A.Shaymaa ,( 2015), principally quasi injective system over monoid , journal of advances in mathematics ,Vol .(10),No.(1) , pp.3152-3162.

M.S.Abbas and A.Shaymaa , (2015 ) , quasi principally injective systems over monoids , journal of advances in mathematics ,Vol .(10),No.(5) , pp.3493-3502.

M.S. Abbas and A. A.Mustafa , (2015 ) , fully pseudo stable systems , journal of advances in mathematics ,Vol .(10),No.(3) , pp. 3356-3361.

M.Ershad , M.Roueentan and M.A.Naghipoor , (2012) , On C-injectivity of acts over monoids, 22nd Iranian Algebra seminar , pp. 94-97.

P . Berthiaume , (1967) , The injective envelope of S-sets ,Canad . Math. Bull., 10, pp.261 – 273.

R.Mohammad and E.Majid , (2014 ) ,Strongly duo and duo right S-acts , Italian journal of pure and applied mathematics,32, pp.143-154.

R.B.Hiba , (2014 ) , On fully stable acts . MSC thesis , College of Science , Univ. of Al-Mustansiriyah.

T.Yan , (2011) , Generalized injective S-acts on a monoid , Advances in mathematics , Vol.40,No.4,pp. 421-432.

T.Yan , A.Javed , X.FEI and G.XIAO,( 2007), Monoids characterized by their injectivity and projectivity classes , Advances in mathematics , Vol.36,No.3 ,pp. 321-326.

*Journal of Progressive Research in Mathematics*,

*4*(2), 321-327. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/255

Copyright (c) 2015 Journal of Progressive Research in Mathematics

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.