ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

Title & Authors
ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS
Badawi, Ayman; Tekir, Unsal; Yetkin, Ece;

Abstract
Let R be a commutative ring with $\small{1{\neq}0}$. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, $\small{c{\in}R}$ and $\small{0{\neq}abc{\in}I}$, then $\small{ab{\in}I}$ or $\small{ac{\in}\sqrt{I}}$ or $\small{bc{\in}\sqrt{I}}$. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 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;
Language
English
Cited by
1.
ON n-ABSORBING IDEALS AND THE n-KRULL DIMENSION OF A COMMUTATIVE RING, Journal of the Korean Mathematical Society, 2016, 53, 6, 1225
2.
ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS, Journal of the Korean Mathematical Society, 2016, 53, 3, 549
3.
Weakly Classical Prime Submodules, Kyungpook mathematical journal, 2016, 56, 4, 1085
4.
On n-absorbing submodules of modules over commutative rings, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016, 57, 3, 679
5.
On (m, n)-absorbing ideals of commutative rings, Proceedings - Mathematical Sciences, 2017, 127, 2, 251
References
1.
D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra 36 (2008), no. 2, 686-696.

2.
D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math. 29 (2003), no. 4, 831-840.

3.
D. F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (2011), no. 5, 1646-1672.

4.
S. Ebrahimi Atani and F. Farzalipour, On weakly primary ideals, Georgian Math. J. 12 (2005), no. 3, 423-429.

5.
A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), no. 3, 417-429.

6.
A. Badawi and A. Y. Darani, On weakly 2-absorbing ideals of commutative rings, Houston J. Math. 39 (2013), no. 2, 441-452.

7.
A. Badawi, U. Tekir, and E. Yetkin, On 2-absorbing primary ideals in commutativerings, Bull. Korean Math. Soc. (in press)

8.
A. Y. Darani and E. R. Puczylowski, On 2-absorbing commutative semigroups and their applications to rings, Semigroup Forum 86 (2013), no. 1, 83-91.

9.
M. Ebrahimpour and R. Nekooei, On generalizations of prime ideals, Comm. Algebra 40 (2012), no. 4, 1268-1279.

10.
R. Gilmer, Multiplicative Ideal Theory, Queen's Papers Pure Appl. Math. 90, Queen's University, Kingston, 1992.

11.
J. Huckaba, Rings with Zero-Divisors, New York/Basil: Marcel Dekker, 1988.

12.
S. Payrovi and S. Babaei, On the 2-absorbing ideals, Int. Math. Forum 7 (2012), no. 5-8, 265-271.