• Korean Journal of Mathematics
• /
• 제13권1호
• /
• pp.13-18
• /
• 2005

Recently, Kehayopulu and Tsingelis studied for prime ideals of groupoids-ordered groupoids. In this paper, we give some results on prime left(right) ideals of groupoid-ordered groupoid. These results are generalizations of their results.

• 대한수학회논문집
• /
• 제13권2호
• /
• pp.251-256
• /
• 1998

We introduce the concept of weakly prime ideals in po-$\Gamma$-semigroup and give some characterizations of weakly prime ideals.

• 호남수학학술지
• /
• 제29권4호
• /
• pp.667-679
• /
• 2007

We study the prime ideal structure of the direct sum of directed system of rings indexed by a commutative semigroup which is nilpotent extension of a group.

• 호남수학학술지
• /
• 제27권3호
• /
• pp.333-341
• /
• 2005

A characterization of prime ideals is discussed. A relation between prime ideals and ideals of the form $A_w^{\wedge}$ is given. The prime ideal theorem is established. The notion of annihilators is introduced, and basic properties are investigated.

• East Asian mathematical journal
• /
• 제22권2호
• /
• pp.239-248
• /
• 2006

Let G be a group acting on a ring R. We will define the group action of G on an intuitionsitic fuzzy set of R. We will introduce intuitionistic fuzzy G-prime ideals of a ring and we will prove that every intuitionistic fuzzy G-prime ideal is the largest G-invariant intuitionistic fuzzy ideal of R contained in the intuitionistic fuzzy prime ideal which is uniquely determined up to G-orbits.

• 대한수학회보
• /
• 제45권4호
• /
• pp.797-800
• /
• 2008

Let R be a ring and I be a proper ideal of R. For the case of R being commutative, Anderson proved that (*) there are only finitely many prime ideals minimal over I whenever every prime ideal minimal over I is finitely generated. We in this note extend the class of rings that satisfies the condition (*) to noncommutative rings, so called homomorphically IFP, which is a generalization of commutative rings. As a corollary we obtain that there are only finitely many minimal prime ideals in the polynomial ring over R when every minimal prime ideal of a homomorphically IFP ring R is finitely generated.

• 충청수학회지
• /
• 제26권4호
• /
• pp.703-706
• /
• 2013

Let R be a commutative noetherian algebra and let ${\delta}$ be a nonzero derivation. Here we determine the prime ideals of the skew polynomial algebra R[z;${\delta}$] and the Poisson prime ideals of R[z;${\delta}$]p.

• 대한수학회보
• /
• 제44권1호
• /
• pp.151-156
• /
• 2007

A connection between weak ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

• East Asian mathematical journal
• /
• 제19권2호
• /
• pp.233-240
• /
• 2003

Xie and Wu introduced an m-system in a po-semigroup. Kehayopulu gave characterizations of weakly prime ideals of po-semigroups and Lee and Kwon add two characterizations for weakly prime ideals. In this paper, we give a characterization of weakly prime ideals and a characterization of weakly semi-prime ideals in po-semigroups using m-system and n-system, respectively

• 대한수학회논문집
• /
• 제11권2호
• /
• pp.315-321
• /
• 1996

Recently, N. Kehayopulu [4] introduced the concepts of weakly prime ideals of ordered semigroups. In this paper, we define the concepts of left(right) weakly prime and left(right) semiregular. Also we investigate the properties of them.