• Communications of the Korean Mathematical Society
• /
• v.11 no.4
• /
• pp.895-902
• /
• 1996

In this paper, we describe the ideal generated by non-empty stable set in a BCI-group as a simple form, and obtain an equivalent condition of prime Z-ideal.

• Honam Mathematical Journal
• /
• v.16 no.1
• /
• pp.63-66
• /
• 1994

• Kyungpook Mathematical Journal
• /
• v.34 no.1
• /
• pp.73-80
• /
• 1994

• Journal of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.207-216
• /
• 1987

• The Mathematical Education
• /
• v.16 no.2
• /
• pp.27-28
• /
• 1978

• East Asian mathematical journal
• /
• v.3
• /
• pp.27-31
• /
• 1987

• East Asian mathematical journal
• /
• v.9 no.1
• /
• pp.105-111
• /
• 1993

• Kyungpook Mathematical Journal
• /
• v.32 no.3_spc
• /
• pp.629-633
• /
• 1992

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.6
• /
• pp.1401-1407
• /
• 2021

Let R be a commutative G-graded ring with a nonzero unity. In this article, we introduce the concept of graded radically principal ideals. A graded ideal I of R is said to be graded radically principal if Grad(I) = Grad(〈c〉) for some homogeneous c ∈ R, where Grad(I) is the graded radical of I. The graded ring R is said to be graded radically principal if every graded ideal of R is graded radically principal. We study graded radically principal rings. We prove an analogue of the Cohen theorem, in the graded case, precisely, a graded ring is graded radically principal if and only if every graded prime ideal is graded radically principal. Finally we study the graded radically principal property for the polynomial ring R[X].

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.259-266
• /
• 2024

The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to r-strongly irreducible r-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are T₀, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize rarithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of r-maximal r-ideals and r-prime r-ideals to be dense in the corresponding terminal spaces.