Ayman BADAWI, Ünsal TEKİR, Emel ASLANKARAYİĞİT UĞURLU, Gülşen ULUCAK, Ece YETKİN ÇELİKEL

310290

Generalizations of 2-absorbing primaryideals of commutative rings

ideals of $R$. In this paper, we extend the concept of 2-absorbing primary ideals to the context of $\phi $-2-absorbing primary ideals. Let $\phi :S(R)\rightarrow S(R)\cup \emptyset $ be a function. A proper ideal $I$ of $% R $ is said to be a $\phi $-2-absorbing primary ideal of $R$ if whenever $% a,b,c\in R$ with $abc\in I-\phi (I)$ implies $ab\in I$ or $ac\in \sqrt{I}$ or $bc\in \sqrt{I}$. A number of results concerning $\phi $-2-absorbing primary ideals are given.
Keywords:

Primary ideal, weakly primary ideal, prime ideal, weakly prime ideal, 2-absorbing ideal, n-absorbing ideal, weakly 2-absorbing ideal 2-absorbing primary ideal, weakly 2-absorbing primary ideal, $\phi $-prime ideal, $\phi $-2-primary ideal, $\phi $-2-absorbing ideal,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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