Let R=⊕ n∈ ℤ 0 R n R=⊕_n∈Z_0R_n be a positively graded ring which is a sub-ring of the
strongly graded ring S=⊕ n∈ ℤ R n S=⊕_n∈ZR_n, where R 0 is a Noetherian prime ring. It …

Let R be a commutative ring with identity. A proper ideal I of R is said to be 1-absorbing
prime ideal if whenever xyz∈ I for some nonunit elements x, y, z∈ R, then either xy∈ I or …

Non-commutative unique factorization rings with zero-divisors Page 1 Journal of Algebra
and Its Applications Vol. 20, No. 2 (2021) 2150022 (6 pages) c© World Scientific Publishing …

Let R be a commutative ring with identity. A proper ideal I of R is said to be 2-absorbing if
whenever xyz∈ I for some elements x, y, z∈ R, then either xy∈ I or xz∈ I or yz∈ I. The ring …

We call a prime Noetherian maximal order R a pseudo-principal ring if every reflexive ideal
of R is principal. This class of rings is a broad class properly containing both prime …

Suppose that K is a field, S= K [x 1,…, xn] or S= K [[x 1,…, xn]] and I is a monomial ideal of S.
We study factorization properties of the ring R= S/I. In particular, we present conditions …

Given a certain factorization property of a ring R, we can ask if this property extends to the
polynomial ring over R or vice versa. For example, it is well known that R is a unique …

If R is right pseudo-Frobenius (= PF), and A is an ideal, when is R/A right PF? Our main
result, Theorem 3.7, states that this happens iff the ideal A′ of the basic ring B of R …

Let R be a commutative ring with identity. A proper ideal P of R is a weakly prime ideal if 0≠
ab∈ P implies a∈ P or b∈ P. Weakly prime ideals arose from the study of factorization in …

Let R be a commutative ring with identity. A proper ideal P of R is an almost prime ideal if
ab∈ PP 2 implies a∈ P or b∈ P. A proper ideal P of R is a weakly prime ideal if 0≠ ab∈ P …