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61
On MLGP- Rings
Raida D.mahmood Ebtehal S. Mageed
raida.1961@uomosul.edu.iq
College of Computer Sciences and Mathematics
University of Mosul, Mosul, Iraq
ABSTRACT
An ideal of a ring is called right (left) generalized pure (-ideal)if for every
, there exists , and such that ( ) . A ring
is called - ring if every right maximal ideal is left - ideal . In this paper have
been studied some new properties of - rings and the relation between this rings
and strongly - regular rings some of the main result of the present work are as follows:
1- Let be a local , and ring . Then :
(a) .
(b) If is - ring . Then is a direct sum and for all , .
2 - Let be a local , and - ring . Then is strongly - regular if and only
if i .
Keywords: NJ Rings , SXM rings ,local strongly regular rings ,pure ideals
MLGP-
1806\2019 30062019
(1)
a
b
MLGP-
62
(2)
NJSXM
1Introduction
.2
2.1
2
3.1.45
1
▄
63
2.2
≠0
▄
2.3
1
2
3
4
5
6
7
1232
2.101133445
671.33732.2▄
2.4
MLGP-
64
2.5
1
2
1
4
2
3.1.25
▄
2.6
1
2
12.5 1.33
21 ▄
2.7
65
▄
1
2.8
▄
MLGP-
66
Abdullah , H. Handan , K. and Bureu , U. (2018 ), " On Weak symmetric
property of rings" , Sou . Asian , Bull . of Math . 42 , pp 31 – 40 .
[1]
on , D.M. (1970) ; "",
.
[2]
Chang ,L. and Soo, Y. p. (2018) " When nilpotents are contanined in
Jacobson radicals " J . Korean . Math . Soc . 55 , No .5, pp , 1193-1205 .
[3]
Hazewinkel , M . , Gubareni , N . and Kiriehenko V. V. , (2004) , "
Algebras , Rings and Modules " Vol .1 Kluwer Academic publishers .
[4]
, . . (2000) , " When
nilpotents are contanined in Jacobson radicals " , .. , ,
.
[5]
Maximal generalization of
pure ideals "
[6]
Wei , J. C. (2007) , " On simple singular YJ-injective modules " , Sou.
Asian Bull . Of Math. 31, pp.1-10 .
[7]
