IRREDUCIBLE IDEALS IN RINGS

B. Venkateswarlu; R. Vasu Babu; Tigist Embiale

IRREDUCIBLE IDEALS IN RINGS

Autori

B. Venkateswarlu GIT, GITAM University - Department of Mathematics
R. Vasu Babu Shri Vishnu Engineering College for Women - Department of Mathematics
Tigist Embiale Gondar University - Department of Mathematics

Parole chiave:

α−irreducible, α−strongly irreducible, compact element, algebraic lattice, ascending chain condition, module over a ring

Abstract

It is well known that the ideals of any ring form an algebraic lattice under the set inclusion ordering, in which the finitely generated ideals are precisely the compact elements. Strongly irreducible ideals of a ring were studied by W.J. Heinzer, L.J. Ratliff and D.E. Rush [3] and α−irreducible and α−strongly irreducible ideals of a ring were characterized by X. Lu and H. Qin [8]. In this paper, we extend these results for elements of a general algebraic lattice and obtain the results on ideals of rings and on submodules of an R−module as consequences of our general results. Also, we characterize algebraic lattices satisfying the ascending chain condition.

Cover of n°32 Italian Journal of Pure and Applied Mathematics

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Pubblicato

2014-08-22

Come citare

Venkateswarlu, B., Vasu Babu, R., & Embiale, T. (2014). IRREDUCIBLE IDEALS IN RINGS. Italian Journal of Pure and Applied Mathematics, 32, 461–466. Recuperato da https://journals.uniurb.it/index.php/ijpam/article/view/6188