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519 results on '"ZHOU, YIQIANG"'

167. Rings whose cyclics are -modules.

Author

Ibrahim, Yasser, Nguyen, Xuan Hau, Yousif, Mohamed F., and Zhou, Yiqiang

Subjects
MODULES (Algebra), QUASIGROUPS, RING theory, MATHEMATICAL analysis, SEMISIMPLE Lie groups
Abstract

It is well known that if every cyclic right module over a ring is injective, then the ring is semisimple artinian. This classical theorem of Osofsky promoted a considerable interest in the rings whose cyclics satisfy a certain generalized injectivity condition, such as being quasi-injective, continuous, quasi-continuous, or . Here we carry out a study of the rings whose cyclic modules are -modules. The motivation is the observation that a ring is semisimple artinian if and only if every -generated right -module is a -module. Many basic properties are obtained for the rings whose cyclics are -modules, and some structure theorems are proved. For instance, it is proved that a semiperfect ring has all cyclics -modules if and only if it is a direct product of a semisimple artinian ring and finitely many local rings, and that a right self-injective regular ring has all cyclics -modules if and only if it is a direct product of a semisimple artinian ring, a strongly regular ring and a matrix ring over a strongly regular ring. Applications to the rings whose -generated modules are -modules, and the rings whose cyclics are ADS or quasi-continuous are addressed. [ABSTRACT FROM AUTHOR]

Published
2016
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168. -projective dimensions, Foxby equivalence and -projective modules.

Author

Zhao, Liang and Zhou, Yiqiang

Subjects
*DIMENSION theory (Algebra), *MATHEMATICAL equivalence, *PROJECTIVE modules (Algebra), *QUASI-Frobenius rings, *FIELD extensions (Mathematics)
Abstract

This is a study of Ding projective modules relative to a semidualizing module and related topics. Firstly, we study -projective dimensions and -projective modules under change of rings. Secondly, we establish a new version of the Foxby equivalence with respect to -projective modules and -injective modules. Thirdly, we characterize Ding projective modules in and Ding injective modules in . At last, as applications, some new characterizations of perfect rings and quasi-Frobenius rings are given. [ABSTRACT FROM AUTHOR]

Published
2016
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170. GENERALISED ARMENDARIZ PROPERTIES OF CROSSED PRODUCT TYPE.

Author

ZHAO, LIANG and ZHOU, YIQIANG

Subjects
RING theory, MONOIDS, POLYNOMIALS, HOMOMORPHISMS, MULTIPLICATION
Abstract

Let R be a ring and M a monoid with twisting f:M × M → U(R) and action ω: M→ Aut(R). We introduce and study the concepts of CM-Armendariz and CM-quasi-Armendariz rings to generalise various Armendariz and quasi-Armendariz properties of rings by working on the context of the crossed product R*M over R. The following results are proved: (1) If M is a u.p.-monoid, then any M-rigid ring R is CM-Armendariz; (2) if I is a reduced ideal of an M-compatible ring R with M a strictly totally ordered monoid, then R/I being CM-Armendariz implies that R is CM-Armendariz; (3) if M is a u.p.-monoid and R is a semiprime ring, then R is CM-quasi-Armendariz. These results generalise and unify many known results on this subject. [ABSTRACT FROM AUTHOR]

Published
2016
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