• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.241-248
• /
• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Journal of the Chungcheong Mathematical Society
• /
• 제26권4호
• /
• pp.923-926
• /
• 2013

We find congruence properties on the coefficients of modular forms for ${\Gamma}^+_0(5)$ generated by ${\Gamma}_0(5)$ and a Fricke involution $\(_{5\;0}^{0\;-1}\)$.

• Honam Mathematical Journal
• /
• 제32권4호
• /
• pp.791-795
• /
• 2010

We study the consequences of Gross's conjecture for cyclic extensions of degree $l^2$ where l is prime, and deduce that the L-values at s = 0 satisfy certain congruence relations.

• Journal of applied mathematics & informatics
• /
• 제8권1호
• /
• pp.1-8
• /
• 2001

We show that all automata in a. certain natural class satisfy three semisimplicity properties and describe all languages recognized by these automata.

• Kyungpook Mathematical Journal
• /
• 제46권2호
• /
• pp.247-253
• /
• 2006

(Left or Right) Weakly commutative semigroups are described. Relationships of weakly commutative semigroups and (l- or r-) Archimedean semigroups are discussed. The structure theorems of weakly commutative semigroups and weakly commutative abundant semigroups are shown.

• Journal of the Chungcheong Mathematical Society
• /
• 제23권4호
• /
• pp.823-826
• /
• 2010

Let p be a prime. We generalized Sturm's bound to a group ${\Gamma}_{0}^{+}(p)$ of which the genus is zero.

• Journal of the Korean Mathematical Society
• /
• 제60권5호
• /
• pp.1073-1085
• /
• 2023

A partition of n is called a t-core partition if none of its hook number is divisible by t. In 2019, Hirschhorn and Sellers [5] obtained a parity result for 3-core partition function a3(n). Motivated by this result, both the authors [8] recently proved that for a non-negative integer α, a3αm(n) is almost always divisible by an arbitrary power of 2 and 3 and at(n) is almost always divisible by an arbitrary power of pji, where j is a fixed positive integer and t = pa11pa22···pamm with primes pi ≥ 5. In this article, by using Hecke eigenform theory, we obtain infinite families of congruences and multiplicative identities for a2(n) and a13(n) modulo 2 which generalizes some results of Das [2].

• Communications of the Korean Mathematical Society
• /
• 제24권3호
• /
• pp.341-351
• /
• 2009

The notion of rough sets was introduced by Z. Pawlak in the year 1982. The notion of a $\Gamma$-semigroup was introduced by M. K. Sen in the year 1981. In 2003, Y. B. Jun studied the roughness of sub$\Gamma$-semigroups, ideals and bi-ideals in i-semigroups. In this paper, we study rough prime ideals and rough fuzzy prime ideals in $\Gamma$-semigroups.

• Communications of the Korean Mathematical Society
• /
• 제23권4호
• /
• pp.479-485
• /
• 2008

In this note, we study arithmetic properties for the exponents of modular forms on ${\Gamma}_0(p)$ for primes p. Our aim is to refine the result of [4] by using the geometric property of the modular curve of ${\Gamma}_0(p)$.

• Communications of the Korean Mathematical Society
• /
• 제20권3호
• /
• pp.467-485
• /
• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$