TITLE

When is a Quasi-p-injective Module Continuous?

AUTHOR(S)
Chotchaisthit, Somchit
PUB. DATE
September 2002
SOURCE
Southeast Asian Bulletin of Mathematics;2002, Vol. 26 Issue 3, p391
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
.It is well-known that every quasi-p-injective module has C2-condition. In this note, it is shown that for a quasi-p-injective module M which is a self-generator, if M is projective, duo and semiperfect, then M is continuous. As a special case we re-obtain a result of Puninski-Wisbauer-Yousif saying that, a semiperfect ring R is right continuous if it is right duo, right p-injective.
ACCESSION #
9943810

 

Related Articles

  • In a Right Perfect Right Self-Injective Ring Right PF? Nguyen Thi Bach Kim // Vietnam Journal of Mathematics;Dec2000, Vol. 28 Issue 4, p321 

    Examines the formulations of right perfect right self-injective ring R. Sufficient conditions for a semiperfect ring; Questions for a right perfect right self-injective ring R; Characterization of a right pseudo-frobenius ring.

  • Principally Small Injective Rings. YUEMING XIANG // Kyungpook Mathematical Journal;Jun2011, Vol. 51 Issue 2, p177 

    A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ? R. A right R-module M is called PS-injective if every R-homomorphism f : aR ? M for every principally small right ideal aR can be extended to R ? M. A ring R is called right PS-injective if R is...

  • A Weaker Form of p-injectivity. Hoang Dinh Hai; Nguyen Van Sanh; Aisuriya Sudprasert // Southeast Asian Bulletin of Mathematics;2009, Vol. 33 Issue 6, p1063 

    Let R be a ring. A right R-module N is called an M-p-injective module if any homomorphism from an M-cyclic submodule of M can be extended to M. In this paper, we extend this notion and investigate the class of M-rp-injective modules and M-lp-injective modules, and prove that for a finitely...

  • Weakly P-injective Rings. Zhanmin, Zhu // Southeast Asian Bulletin of Mathematics;2007, Vol. 31 Issue 3, p615 

    A ring R is called right-right (resp. right-left) weakly P-injective, if, for any 0 ≠ a ∈ R, there exists b ∈ R such that ba ∈ 0 (resp. ab ≠ 0) and any right R-homomorphism from baR (resp. abR) to R extends to an endomorphism of R. In this paper, various properties of...

  • Algebraic cobordisms of a Pfister quadric. A. Vishik; N. Yagita // Journal of the London Mathematical Society;Dec2007, Vol. 76 Issue 3, p586 

    In this article we compute the ring of algebraic cobordisms of a Pfister quadric. This is a rare example of a non-cellular variety where such a computation is known. We consider the algebraic cobordisms O* of Levine and Morel, as well as the MGL2*, * of Voevodsky. The methods of computation in...

  • Some Generalizations of Small Injective Modules. TRUONG CONG QUYNH // Bulletin of the Malaysian Mathematical Sciences Society;2012, Vol. 35 Issue 3, p621 

    Let R be a ring. Let m and n be positive integers, a right R-module M is called (m,n)-small injective, if every right R-homomorphism from an n-generated submodule of Jm to M extends to one from Rm to M. A ring R is called right (m,n)-small injective if the right R module RR is (m,n)-small...

  • ON GENERALIZED EXTENDING MODULES. Kamal, M. A.; Sayed, A. // Acta Mathematica Universitatis Comenianae;2007, Vol. 76 Issue 2, p193 

    H. Hanada, J. Kado, and K. Oshiro have introduced, in a diagram of modules and homomorphisms, the concept of generalized M-injective modules. S. Mohamed, and B. Mueller have given a different characterization, based on an exchange property, of the generalized M-injective modules. Here we...

  • On Quasi-(í’Ž, 풏)-Injective Modules. Zhanmin Zhu; Jianlong Chen; Xiaoxiang Zhang // Southeast Asian Bulletin of Mathematics;2004, Vol. 28 Issue 5, p971 

    Let R be a ring. Given a right R-module M, for two fixed positive integers m and n, a right R-module N is called M-n-generated if it is a homomorphic image of Mn. We call M quasi-(m, n)-injective if each R-homomorphism from an M-n-generated submodule of Mm to M extends to one from Mm to M....

  • Quasi-c-Principally Injective Modules and Self-c-Principally Injective Rings. Chaturvedi, A. K.; Pandeya, B. M.; Gupta, A. J. // Southeast Asian Bulletin of Mathematics;2009, Vol. 33 Issue 4, p685 

    In this paper, the concepts of quasi-c-principally injective modules (in short, quasi-cp-injective modules) and self-c-principally injective rings are introduced. In support of these concepts we have also provided the examples. The characterization and some properties of quasi-cp-injective...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics