Co-small Module

Authors

  • Wang Li Longqiao College of Lanzhou Commercial College, Lanzhou 730010, Gansu
  • Cuncheng Jin Longqiao College of Lanzhou Commercial College, Lanzhou 730010, Gansu

DOI:

https://doi.org/10.26713/jims.v7i2.315

Keywords:

Co-small modules, Strong modules, Semisimple and noetherian ring

Abstract

The main goal of the present article is to study basic properties of co-small modules. Let $R$ be a Noetherian ring, For all co-small module $B$ and index $I$, we get isomorphic $Torn(B;\prod A_i)\cong \prod Torn(B;A_i)$. Finally, we prove that If two modules of the sequence $0 \to A\to B\to C\to 0$ are co-small modules, so is the third.

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References

F.W. Anderson and K.R. Fuller, Rings and Categories of Modules, Spring-Verlag, New York, 1974.

D.M. Arnold and C.E. Murley, Abelian groups, $A$, such that Hom$(A;-)$ preserves direct sums of copies of $A$, Pac. J. Math. 56 (1975), 7-20.

S. Breaz and J.M. Zemlicka, When every self-small module is finitely generated, J. Algebra 158 (2007), 400-419.

J.J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.

J.M. Zemlicka, When products of self-small modules are self-small, Comm. Algebra

(7) (2008), 2570-2576.

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Published

2015-11-30
CITATION

How to Cite

Li, W., & Jin, C. (2015). Co-small Module. Journal of Informatics and Mathematical Sciences, 7(2), 87–91. https://doi.org/10.26713/jims.v7i2.315

Issue

Vol. 7 No. 2 (2015)

Section

Research Articles

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