Publication: On weakly 2-prime ideals in commutative rings
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Date
2021
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TAYLOR & FRANCIS INC
Abstract
The purpose of the paper is to introduce and study weakly 2-prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity. A proper ideal P of A is said to be a weakly 2-prime ideal if whenever 0 not equal xy is an element of P for some x, y is an element of A, then x(2) is an element of P or y(2) is an element of P: Besides giving various examples and characterizations of weakly 2-prime ideals, we investigate the relations between weakly 2-prime ideals and other classical ideals such as 2-prime ideals, weakly prime ideals and weakly 2-absorbing primary ideals. Furthermore, we study 2-prime avoidance lemma in commutative rings and introduced the class of compactly 2-packed rings. Finally, we investigate the compactly packedness, compactly 2-packedness and coprimely packedness of trivial extension A (sic) M of an A-module M.
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Keywords
Compactly 2-packed ring, compactly packed ring, coprimely packed ring, 2-prime ideal, weakly 2-prime ideal, weakly prime ideal