• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.4
• /
• pp.553-559
• /
• 2015

The purpose of this paper is to show an integrated semigroup on a Banach space can be approximated by a sequence of integrated semigroups acting on different Banach spaces.

• East Asian mathematical journal
• /
• v.21 no.2
• /
• pp.151-161
• /
• 2005

We analyze the structure of $C^*-algebras$ generated by left regular isometric representations of semigroups.

• Honam Mathematical Journal
• /
• v.35 no.4
• /
• pp.583-606
• /
• 2013

We generalize the idea of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered semi-group and give the concept of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered $\mathcal{LA}$-semigroup. We show that (${\in}$, ${\in}{\vee}q_k$)-fuzzy left (right, two-sided) ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy (generalized) bi-ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy interior ideals and (${\in}$, ${\in}{\vee}q_k$)-fuzzy (1, 2)-ideals need not to be coincide in an ordered $\mathcal{LA}$-semigroup but on the other hand, we prove that all these (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideals coincide in a left regular class of an ordered $\mathcal{LA}$-semigroup. Further we investigate some useful conditions for an ordered $\mathcal{LA}$-semigroup to become a left regular ordered $\mathcal{LA}$-semigroup and characterize a left regular ordered $\mathcal{LA}$-semigroup in terms of (${\in}$, ${\in}{\vee}q_k$)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideal theory by using the notions of duo and (${\in}{\vee}q_k$)-fuzzy duo.

• Journal of applied mathematics & informatics
• /
• v.8 no.1
• /
• pp.273-283
• /
• 2001

We introduce sums and joins of T-fuzzy transformation semi-groups and investigate their algebraic structures.

• Korean Journal of Mathematics
• /
• v.10 no.2
• /
• pp.117-122
• /
• 2002

In this paper, we give some properties of left(right) semi-regular and $g$-regular $po$-semigroups.

• Korean Journal of Mathematics
• /
• v.10 no.2
• /
• pp.191-194
• /
• 2002

Let $S_i$ be the numerical semigroup generated by the set $\{a,a+d,{\cdots},a+(i-1)d,a+(i+1)d, {\cdots},a+rd\}$. In this paper, we will formulate the largest nonmember, the Frobenius number, of each set $S_i$.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.465-475
• /
• 2012

We characterize the fuzzy ideal generated by a fuzzy subset in a semigroup and the fuzzy interior ideal generated by a fuzzy subset in a semigroup. Our work generalizes the characterizations ([8]) of those fuzzy ideals generated by fuzzy subsets in semigroups with an identity element.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.187-191
• /
• 1996

Let C be a nonsingular complex projective algebraic curve (or a compact Riemann surface) of genus g. Let $M(C)$ denote the field of meromorphic functions on C and N the set of all non-negative integers.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.175-182
• /
• 2001

In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation with nonlocal condition using the semigroup theory and the Banach fixed point principle.