Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...

If I is a monomial ideal with linear quotients, then it has componentwise quotients. However, the converse of this statement an open question. In paper, we provide two classes ideals for which holds. First class polymatroidal in K[x, y] and second one strong exchange property.

This paper presents an algorithm for the Quillen-Suslin Theorem for quotients of polynomial rings by monomial ideals, that is, quotients of the form A = kx 0 ; :::;xn]=I, with I a monomial ideal and k a eld. T. Vorst proved that nitely generated projective modules over such algebras are free. Given a nitely generated module P, described by generators and relations, the algorithm tests whether P...

An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection. The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexi...

We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semi...

This paper initiates the study of the algebra of quotients associated with a given BCK-algebra, analogous to the classical rings of quotients and their subsequent generalizations. MIRAMAKE TRIESTE August 198B * To appear in "Hath. Japonlca" (1988). ** Permanent address: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan.

For integers k ≥ 2, we consider the integrality of quotients of Wronskians involving certain normalizations of the Andrews-Gordon q-series (see [2]) ∏ 1≤n "≡ 0,±i (mod 2k+1) 1 1 − qn . This study is motivated by the appearance of these series in conformal field theory as irreducible characters of Virasoro minimal modules. We establish an upper bound on primes p for which such quotients of Wrons...

For positive integers k ≥ 2, we consider the integrality of quotients of Wronskians involving certain normalizations of the Andrews-Gordon q-series ∏ 1≤n 6≡0,±i(mod2k+1) 1 1− qn . This study is motivated by the appearance of these series in conformal field theory as irreducible characters of Virasoro minimal modules. We establish an upper bound on primes p for which such quotients of Wronskians...