On rings whose finitely generated left ideals are left annihilators of an element

Details On rings whose finitely generated left ideals are left annihilators of an element On rings whose finitely generated left ideals are left annihilators of an element

2010-02-17

arxiv.org/abs/1002.3193v2

Mathematics

Rings and Algebras

20 pages, 4 figures. Comments are very welcome(email:xiande.yang@gmail.com). This is a revised version of Feb 2010 arxiv:100

Scientific paper

An associative ring $R$ with identity is left pseudo-morphic if for every $a$$\in$$R$, there exists $b$$\in$$R$ such that $Ra=l_R(b)$. If, in addition, $l_R(a)=Rb$, then $R$ is called left morphic. $R$ is morphic if it is both left and right morphic. We characterize left pseudo-morphic rings; identify the cases a (left) pseudo morphic ring is (left) quasi-morphic, morphic, Quasi-Frobenius, von Neumann regular, etc.; correct two results in a book and a paper; and completely determine when the trivial extension of a commutative domain is morphic which positively answered a question in a paper.

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