Journal ArticleDOI
On the prime radical of a module over a commutative ring
James Jenkins,Patrick F. Smith +1 more
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In this paper, the prime radical of a module over a commutative ring is studied and discussed in the context of algebraic topology, and the authors show that it can be computed in polynomial time.Abstract:
(1992). On the prime radical of a module over a commutative ring. Communications in Algebra: Vol. 20, No. 12, pp. 3593-3602.read more
Citations
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On the spectrum of a module over a commutative ring
TL;DR: In this paper, the spectrum of a module over a commutative ring has been studied in the context of algebraic communication in algebraic networks, where the spectrum is defined as
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On the prime submodules of multiplication modules
TL;DR: In this paper, the notion of multiplication modules over a commutative ring with identity was introduced, and the product of two submodules of such modules was characterized by the Nakayama lemma.
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Primary modules over commutative rings
TL;DR: In this article, it was shown that if R is a commutative domain which is either Noetherian or UFD, then R is one-dimensional if and only if every (finitely generated) primary R-module has a prime radical.
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On weakly prime radical of modules and semi-compatible modules
TL;DR: In this article, the weakly prime radicals of modules over a commutative ring were defined, and it was shown that any projective module over such a ring is semi-compatible.
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A generalization of baer's lower nilradical for modules
TL;DR: In this paper, the Baer-McCoy radicals of general modules were generalized to the case of left R-modules, and it was shown that for any projective R-module M, cl.radR(M) = Nil*(RM) = Rad(R) = Jac(R), where R is a commutative Noetherian domain.
References
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Modules over Dedekind rings and valuation rings
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On radicals of submodules of finitely generated modules
Roy L. McCasland,Marion E. Moore +1 more
TL;DR: In this paper, the concept of the M-radical of a submodule B of an R-module A is discussed and the main result is that if denotes the ideal radical of (B:A), then M-rad B = provided that A is a finitely generated multiplication module.