Affiliation:
1. Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa, Jordan
Abstract
Let R be a commutative ring with unity (1 ? 0) and let J(R) be the set of all
ideals of R. Let ? : J(R) ? J(R) ? {?} be a reduction function of ideals of
R and let ? : J(R) ? J(R) be an expansion function of ideals of R. We recall
that a proper ideal I of R is called a ? -1-absorbing ?-primary ideal of R,
if whenever abc ? I ? ? (I) for some nonunit elements a, b, c ? R, then ab ?
I or c ? ?(I). In this paper, we introduce a new class of ideals that is a
generalization to the class of ?-1-absorbing ?-primary ideals. Let S be a
multiplicative subset of R such that 1 ? S and let I be a proper ideal of R
with S ? I = ?, then I is called a ?-S-1-absorbing ?-primary ideal of R
associated to s ? S, if whenever abc ? I? ?(I) for some nonunit elements a,
b, c ? R, then sab ? I or sc ? ?(I). In this paper, we have presented a
range of different examples, properties, characterizations of this new class
of ideals.
Publisher
National Library of Serbia