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On Radicals of Submodules of Finitely Generated Modules

Published online by Cambridge University Press:  20 November 2018

Roy L. McCasland  and
Marion E. Moore
Roy L. McCasland
Affiliation:
Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
Marion E. Moore
Affiliation:
Department of Mathematics, University of Texas at ArlingtonArlington, Texas76019
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Abstract

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The concept of the M-radical of a submodule B of an R-module A is discussed (R is a commutative ring with identity and A is a unitary fl-module). The M-radical of B is defined as the intersection of all prime submodules of A containing B. The main result of the paper is that if denotes the ideal radical of (B:A), then M-rad B = provided that A is a finitely generated multiplication module. Additionally, it is shown that if A is an arbitrary module, where for some

Keywords

13C99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 37 - 39
Copyright
Copyright © Canadian Mathematical Society 1986

References

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4. Zariski, O. and Samuel, P., Commutative Algebra, Vol. I., 1958.Google Scholar