• 대한수학회지
• /
• 제53권2호
• /
• pp.381-401
• /
• 2016

According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and ${\sigma}:M{\rightarrow}End(R)$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and ${\sigma}:M{\rightarrow}End(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

• Kyungpook Mathematical Journal
• /
• 제50권2호
• /
• pp.329-336
• /
• 2010

In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule. Indeed we prove : 1) The quotient semimodule M=N(Q) is essentially independent of choice of Q. 2) If f : M ${\rightarrow}$ M' is a maximal R-semimodule homomorphism, then $M/kerf_{(Q)}\;\cong\;M'$. 3) Every partitioning subsemimodule is subtractive. 4) Let N be a Q-subsemimodule of an R-semimodule M. Then A is a subtractive subsemimodule of M with $N{\subseteq}A$ if and only if $A/N_{(Q{\cap}A)}\;=\;\{q+N:q{\in}Q{\cap}A\}$ is a subtractive subsemimodule of $M/N_{(Q)}$.

• 대한수학회보
• /
• 제57권3호
• /
• pp.803-813
• /
• 2020

Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M⨂_R M^∗ → Hom_R(Hom_R(M, M), R) is a surjective homomorphism. Particularly, if G-gldim(R) ⩽ ∞ and Extⁱ_R(M, M) = 0 (i ⩾ 1), then M is projective.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제10권1호
• /
• pp.4-5
• /
• 1972

이 논문은 modules 사이의 homomorphisms의 exact sequence에서 다음과 같은 것을 밝힌 것임. 1. (equation omitted)이 하나의 exact sequence 이고 P가 임의의 R-module일 때 (equation omitted)은 abelian group의 하나의 exact sequence라는 것. 2. (equation omitted)이 exact sequence 이고 P가 임의의 R-modele이면 (equation omitted)는 abelian group의 하나의 exact sequence라는 것.

• 전자공학회논문지S
• /
• 제36S권6호
• /
• pp.9-16
• /
• 1999

이 논문에서는 렘펠의 D-준동현사상을 바탕으로 하여 드브루인 수열을 만드는 효과적인 알고리즘을 제안한다. 이 알고리즘에서는 k차 드브루인 수열에서 n차 드브루인 수열의 다음 비트을 만드는데 필요한 배타논리합 연산수는, r의 2진 표현에서 1의 갯수를 W(r)이라 쓸 때, $k(2^{W(n-k)}-1)$쯤임을 보인다: 딸서, 드브루인 함수를 잘 고르면 이 수는 k가 된다.

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.347-352
• /
• 2012

In this paper, we denote that $R$ is a near-ring and $G$ an $R$-group. We initiate the study of faithful $R$-group, the substructures of $R$ and $G$, also quotients of substructure relations between them. Next, we investigate some isomorphic properties of near-rings and $R$-groups.

• Kyungpook Mathematical Journal
• /
• 제54권3호
• /
• pp.471-476
• /
• 2014

Let R be a ring. A right R-module M is PS-injective if every R-homomorphism $f:aR{\rightarrow}M$ for every principally small right ideal aR can be extended to $R{\rightarrow}M$. We investigate, in this paper, rings whose simple singular modules are PS-injective. New characterizations of semiprimitive rings and semisimple Artinian rings are given.

• 대한수학회보
• /
• 제26권2호
• /
• 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.

• 한국지능시스템학회논문지
• /
• 제17권3호
• /
• pp.423-429
• /
• 2007

We define and study the fuzzy Jacobson radical of a ${\kappa}$-semiring. Also it is shown that the Jacobson radical of the quotient semiring R/FJR(R) of a ${\kappa}$-semiring by the fuzzy Jacobson radical FJR(R) is semisimple. And the algebraic properties of the fuzzy ideals FJR(R) and FJR(S) under a homomorphism from R onto S are also discussed.

• 대한수학회보
• /
• 제59권1호
• /
• pp.213-226
• /
• 2022

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I ⊗_R M → R ⊗_R M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.