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PRIME AND IRREDUCIBLE PRERADICALS

FRANCISCO RAGGI

Instituto de Matemáticas, UNAM, Area de la Investigación Científica, Circuito Exterior, C.U.,04510, México, D.F, México

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JOSÉ RÍOS

Instituto de Matemáticas, UNAM, Area de la Investigación Científica, Circuito Exterior, C.U.,04510, México, D.F, México

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HUGO RINCÓN

Facultad de Ciencias, UNAM, Circuito Exterior, C.U., 04510, México, D.F, México

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ROGELIO FERNÁNDEZ-ALONSO

Dept. de Matemáticas, UAM-I, Sn. Rafael Atlixco 186, Col. Vicentina, 09340, México D.F, México

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CARLOS SIGNORET

Dept. de Matemáticas, UAM-I, Sn. Rafael Atlixco 186, Col. Vicentina, 09340, México D.F, México

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https://doi.org/10.1142/S0219498805001290Cited by:27 (Source: Crossref)

Abstract

In this paper we study prime preradicals, irreducible preradicals, ∧-prime preradicals, prime submodules and diuniform modules. We study some relations between these concepts, using the lattice structure of preradicals developed in previous papers. In particular, we give a characterization of prime preradicals using an operator named the relative annihilator. We also characterize prime submodules by means of prime preradicals. We give some characterizations of rings that have certain conditions on prime radicals and on irreducible preradicals, such as left local left V-rings, as well as 1-spr rings, which we introduce.

Keywords:

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