Can I read A Note On Y J-injectivity on EtoBox?

A Note On Y J-injectivity by Roger Yue Chi Ming is a Mathematics article available to read on EtoBox.

What is A Note On Y J-injectivity about?

In [ll],p-injective modules are introduced to study von Neumann regular rings and associated rings. In [13], this concept is weakened to Y J-injectivity. ## Recall that (1) A left A-module M is p-injective if, for any principal left ideal P of A, every left A-homomorphism of P into M extends to A; (2) AM is Y J-injective if, for any 0 / a S A, there exist a positive integer n (depending on a) such that a n ^ 0 and every left Ahomomorphism of Aa n into M extends to A. A is called left Y J-injective if ¿A is YJ-injective. P-injectivity and YJinjectivity are similarly defined on the right side. We may note the following results on Y J-injectivity [13] : (a) A is left Y J-injective iff for any 0 / a € A, there exist a positive integer n such that a n A is a non-zero right annihilator; (b) If A is left YJ-injective, the Jacobson radical coincides with the left singular ideal of A; (c) A is quasi-Frobeniusean iff A is right Artinian, left and right Y J-injective. Throughout, A denotes an associative ring with identity and Amodules are unital. J, Z will stand respectively for the Jacobson radical and the left singular ideal of A. A left (right) ideal of A is called reduced if it contains

Who reads A Note On Y J-injectivity?

Author

Roger Yue Chi Ming

Publisher

Walter de Gruyter GmbH

Published

1997

Language

EN

Field

Mathematics (Physical Sciences)