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On Radicals of Submodules of Finitely Generated Modules

  • Roy L. McCasland (a1) and Marion E. Moore (a2)

Abstract

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

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Copyright

References

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1. Bass, H., Algebraic K-Theory, New York, Q.A. Inc., 1968.
2. Hungerford, Thomas W., Algebra, New York, Springer-Verlag, 1974.
3. McCasland, Roy L., Dissertation, University of Texas at Arlington, 1983.
4. Zariski, O. and Samuel, P., Commutative Algebra, Vol. I., 1958.
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