On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring.

SOHEILNIA, FATEMEH

Let R be a commutative semiring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) primary ideals generalizing of 2- absorbing (resp., weakly 2-absorbing) ideals of semirings. A proper ideal I of R said to be a 2-absorbing (resp., weakly 2-absorbing) primary ideal if whenever a, b, c ϵ R such that abc ϵ I (resp., 0 ≠ abc ϵ I), then either ab ϵ I or bc ϵ √I or ac ϵ √I. Moreover, when I is a Q-ideal and P is a k-ideal of R/I with I ⊆ P, it is shown that if P is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R, then P/I is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R/I and it is also proved that if I and P/I are weakly 2- absorbing primary ideals, then P is a weakly 2-absorbing primary ideal of R.

SEMIRINGS (Mathematics); RING theory; IDEALS (Algebra); MATHEMATICAL analysis; COMMUTATIVE rings

Kyungpook Mathematical Journal, 2016, Vol 56, Issue 1, p107

1225-6951

Academic Journal

10.5666/KMJ.2016.56.1.107