Characterizations of semirings byp-injective and projective semimodules
作者:
Javed Ahsan,
M. Shabir,
H.J. Weinert,
期刊:
Communications in Algebra
(Taylor Available online 1998)
卷期:
Volume 26,
issue 7
页码: 2199-2209
ISSN:0092-7872
年代: 1998
DOI:10.1080/00927879808826270
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
In this paper we obtain characterizations of classes of semirings byP-injective and projective rightR-semimodules. We prove that a semiringRis von Neumann regular if and only if each cyclic rightR-semimodule isP-injective. Moreover, a commutative semiring R whose principal ideals arek-closed is von Neumann regular if and only if every simpleR-semimodule is PP-injective. We also examine some properties of rightPP-semirings, that is, semirings all of whose principal right ideals are projective. It is shown thatRis a rightPP-semiring if and only if the endomorphism semiring of every cyclic projective rightR-semimodule is rightPP.
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