• Kyungpook Mathematical Journal
• /
• v.61 no.4
• /
• pp.823-830
• /
• 2021

Let {R_i}_i∈I be an infinite family of rings and R = ∏_i∈I R_i their product. In this paper, we investigate the prime spectrum of R by 𝓕-limits. Special attention is paid to relationship between the elements of Spec(R_i) and the elements of Spec(∏_i∈I R_i) use 𝓕-lim, also we give a new condition so that ∏_i∈I R_i is a zero dimensional ring.

• Honam Mathematical Journal
• /
• v.38 no.2
• /
• pp.295-304
• /
• 2016

In this paper we investigate the Artinianness of certain local cohomology modules $H^i_I(N)$ where N is a minimax module over a commutative Noetherian ring R and I is an ideal of R. Also, we characterize the set of attached prime ideals of $H^n_I(N)$, where n is the dimension of N.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.737-746
• /
• 1999

For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.135-137
• /
• 1989

Let R be a Krull domain with field of fractions K. By Br(R) we denote the Brauer group of R. Studying the Kernel of the homomorphism Br(R).rarw.Br(K), Orzech defined Brauer groups Br(M) for different categories M of R-modules [4]. In this paper we show that an algebra A in Br(D) is a maximal order in A K and that the map Br(D).rarw. Br(K) is one to one. We note here few conventions. All rings are Krull domains and all modules will be unitary. By Z we donote the set of height one prime ideals of a Krull domain.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1251-1258
• /
• 2020

This paper establishes a formula changing the ring from a Noetherian local ring A of dimension d > 0 containing the residue field k to the polynomial ring in d variables k[X₁, X₂, …, X_d] for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of A by highest dimensional associated prime ideals of A.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.569-573
• /
• 1996

We study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, [I] = 0 in $A_{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, [P] = 0 in $A_{n-i}(R)$.

• Kyungpook Mathematical Journal
• /
• v.58 no.1
• /
• pp.9-17
• /
• 2018

Let $R ={\oplus}_{n{\in}Z}R_n$ be a graded commutative Noetherian ring and let I be a graded ideal of R and J be an arbitrary ideal. It is shown that the i-th generalized local cohomology module of graded module M with respect to the (I, J), is graded. Also, the asymptotic behaviour of the homogeneous components of $H^i_{I,J}(M)$ is investigated for some i's with a specified property.

• Journal of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.927-938
• /
• 2011

Let G be an abelian monoid with identity e. Let R be a G-graded commutative ring, and M a graded R-module. In this paper we first introduce the concept of graded primal submodules of M an give some basic results concerning this class of submodules. Then we characterize the graded primal ideals of the idealization R(+)M.

• Kyungpook Mathematical Journal
• /
• v.18 no.1
• /
• pp.23-29
• /
• 1978

In [7) Scott has defined C-formation radical for a class C of near rings and has studied its porperties under chain conditions. A natural question that arises is: Does there exist a Lower C-Formation radical class L(M) containing a given class M of ideals of near rings in C? In this paper we answer this by giving. two constructions for L(M) and prove that prime radical is hereditary.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.25-32
• /
• 1994

Let A be a (complex) Banach algebra. The object of the this paper shall be remove the continuity of the derivation in the recently theorems. We prove that every derivation D on A satisfying [D(a), a] ${\in}$ Prad(A) for all a ${\in}$ A maps into the radical of A. Also if ${\alpha}D^3+D^2$ is a derivation for some ${\alpha}{\in}C$ and all minimal prime ideals are closed, then D maps into its radical.