Let M be an Artinian module over the commutative ring A (with nonzero identity) and a p spec A be such that a is a finitely generated ideal of A and aM = M. Also suppose that H = H where H. = M/ (0: a )for i

Given a monoid string rewriting system M , one way of obtaining a complete rewriting system for M is to use the classical Knuth-Bendix critical pairs completion algorithm. It is well known that this algorithm is equivalent to computing a noncommutative Gröbner basis for M . This article develops an alternative approach, using noncommutative involutive basis methods to obtain a complete involuti...

Let $R$ be a commutative ring with identity‎. ‎A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$‎, ‎$a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...

A connected graph G is said to be k-cycle resonant if, for 16 t6 k, any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M -alternating cycle. The concept of k-cycle resonant graphs was introduced by the present authors in 1994. Some necessary and su4cient conditions for a graph to be k-cycle resonant were given. Rece...

Every lattice is the complete join of all its one-element sublattices. In this paper we address the question: Which lattices L have the property that L is finitely join reducible in SubL? That is, when do there exist proper sublattices A, B such that L = A∨B? In particular, could it be that every nontrivial lattice has this property, in which case every element of SubL would be finitely join re...

abstract. let (r,p) be a noetherian unique factorization do-main (ufd) and m be a finitely generated r-module. let i(m)be the first nonzero fitting ideal of m and the order of m, denotedord_r(m), be the largest integer n such that i(m) ⊆ p^n. in thispaper, we show that if m is a module of order one, then either mis isomorphic with direct sum of a free module and a cyclic moduleor m is isomorphi...

Generic realizations of configurations of lines as reducible projective varieties in Pn are constructed numerically. Examples are taken from projections of abstract seminormal configurations and the classical geometry related to Schläfli’s double-six configuration. The ideal defining the homogeneous coordinate ring of a realization is calculated along with its Hilbert Function, identifying whic...

Let ρ f,λ be the residual Galois representation attached to a newform f and prime ideal λ in integer ring of its coefficient field. In this paper, we prove explicit bounds for residue characteristic ideals such that is exceptional, reducible, projective dihedral image, or image isomorphic A4, S4 A5. We also develop criteria check reducibility , leading an algorithm compute exact set λ. have imp...

The paper introduces an approach for crosstalk-free bitpermute-complement (BPC) permutations routing in hybrid optical variable-stage shuffle-exchange networks (SENs) of size where N=2, and the number of stages can vary in . The number of stages should be asserted as required by a given BPC permutation for its admissibility. The crosstalk is caused by interacting of two optical signals within t...