H. Mostafanasab, Ü. Tekir, G. Ulucak, “Uniformly <nobr>$2$</nobr>-absorbing primary ideals of commutative rings”, Algebra Discrete Math., 2020, Volume 29, Issue 2,Pages <nobr>221

RESEARCH ARTICLE

Uniformly $2$-absorbing primary ideals of commutative rings

H. Mostafanasab^a, Ü. Tekir^b, G. Ulucak^c

^a Department of Mathematics and Applications, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
^b Department of Mathematics, Faculty of Science and Arts, Marmara University 34722, Istanbul, Turkey
^c Department of Mathematics, Gebze Technical University, P. K. 14141400 Gebze, Kocaeli, Turkey

Abstract: In this study, we introduce the concept of "uniformly $2$-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of $2$-absorbing primary ideals of commutative rings. Then we investigate some properties of uniformly $2$-absorbing primary ideals of commutative rings with examples. Also, we investigate a specific kind of uniformly $2$-absorbing primary ideals by the name of "special $2$-absorbing primary ideals".

Keywords: uniformly $2$-absorbing primary ideal, Noether strongly $2$-absorbing primary ideal, $2$-absorbing primary ideal.

MSC: Primary 13A15; Secondary 13E05, 13F05

Received: 10.06.2017

Language: English

DOI: 10.12958/adm476