Modules Whose t-Closed Submodules Have a Summand as a Complement |
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| Authors: | Shadi Asgari A. Haghany A. R. Rezaei |
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| Affiliation: | 1. Department of Mathematical Sciences , University of Isfahan , Isfahan , Iranand School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iransh_asgari@ipm.ir;3. Department of Mathematical Sciences , Isfahan University of Technology , Isfahan , Iran |
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| Abstract: | We define and investigate T 11-type modules as a generalization of t-extending modules, and modules satisfying C 11 condition. A module M is said to be T 11-type if every t-closed submodule of M has a complement which is a direct summand. Direct sums of T 11-type modules inherit the property. Some equivalent conditions for a module M to be T 11-type are given. We characterize a module M for which every direct summand satisfies T 11 condition. If R R is T 11-type, then R/Z 2(R R ) is a C 2 ring if and only if it is a von Neumann regular ring. Applying this result, we characterize a right t-extending (resp., finitely Σ-t-extending, or Σ-t-extending) ring R for which R/Z 2(R R ) is von Neumann regular. |
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| Keywords: | C 11 condition Nonsingular and Z 2-torsion modules T 11-type modules T-extending modules |
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