• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.51-62
• /
• 2015

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.327-335
• /
• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost weakly finite conductor if for any two elements a and b in R, there exists a positive integer n such that aⁿR ∩ bⁿR is finitely generated. In this article, we give some conditions for the trivial ring extensions and the amalgamated algebras to be almost weakly finite conductor rings. We investigate the transfer of these properties to trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new families of examples of nonfinite conductor weakly finite conductor rings.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.359-366
• /
• 1996

A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

• Journal of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1333-1354
• /
• 2019

In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.853-868
• /
• 2022

We study the structure of right regular commutators, and call a ring R strongly C-regular if ab - ba ∈ (ab - ba)²R for any a, b ∈ R. We first prove that a noncommutative strongly C-regular domain is a division algebra generated by all commutators; and that a ring (possibly without identity) is strongly C-regular if and only if it is Abelian C-regular (from which we infer that strong C-regularity is left-right symmetric). It is proved that for a strongly C-regular ring R, (i) if R/W(R) is commutative, then R is commutative; and (ii) every prime factor ring of R is either a commutative domain or a noncommutative division ring, where W(R) is the Wedderburn radical of R.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.527-532
• /
• 1998

We study some properties of Schur functor and its sub-functions related to separable algebras and cyclotomic algebras.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.949-957
• /
• 1997

The purpose of this paper is to establish connection between certain complex of modules of generalized fractions and the concept of cosequence in commutative algebra. The main theorem of the paper leads to characterization, in terms of modules of generalized fractions, of regular (co) sequences.

• Journal of the Chungcheong Mathematical Society
• /
• v.2 no.1
• /
• pp.37-44
• /
• 1989

In this paper, it is shown that automatic continuity of derivations on some semi prime Banach algebras can be extended to higher derivations. In particular, we show that if every prime ideal is closed in a commutative semi prime Banach algebra then every higher derivation on it is continuous.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.261-264
• /
• 1994

Throughout this paper, all rings are assumed to be commutative with identity. By a local ring (R, m), we mean a Noetherian ring R which has the unique maximal ideal m. By dim(R) we always mean the Krull dimension of R. Let I be an ideal in a ring R and t an indeterminate over R. Then the Rees algebra R[It] is defined to be(omitted)

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.17-27
• /
• 2013

The notions of the extensions of bipolar fuzzy ideals, bipolar fuzzy prime ideals and bipolar fuzzy commutative ideals in BCK-algebras are introduced, and several properties are investigated.