We prove that every quasi-complete intersection (q.c.i.) ideal is obtained from a pair of nested complete ideals by way flat base change. As by-product we establish rigidity statement for the minimal two-step Tate complex associated to an I in local ring R. Furthermore, define T each R; and result it. The exact if only q.c.i. ideal; this case, resolution R/I free R-modules.

A class of decision problems is Boolean if it is closed under the set–theoretic operations of union, intersection and complementation. The paper introduces new Boolean classes of decision problems based on algebraic constraints imposed on transitions of finite automata. We discuss issues related to specifications of these classes from algebraic, computational and proof–theoretic points of view.

We describe a Schubert like stratification on the Grassmannian of hermitian lagrangian spaces in C ⊕ C which is a natural compactification of the space of hermitian n × n matrices. The closures of the strata define integral cycles and we investigate their intersection theoretic properties. The methods employed are Morse theoretic.

The grassmannian of hermitian lagrangian spaces in C⊕C is natural compactification of the space of hermitian n× n matrices. We describe a Schubert like stratification on this space which has a Morse theoretic origin. We prove that these strata define closed subanalytic currents à la R. Hardt, generating the integral homology of this space, and then we investigate their intersection theoretic pr...

We describe a Schubert like stratification on the Grassmannian of hermitian lagrangian spaces in C ⊕ C which is a natural compactification of the space of hermitian n × n matrices. The closures of the strata define integral cycles and we investigate their intersection theoretic properties. The methods employed are Morse theoretic.

In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...

This article indicates another set-theoretic formula, solely in terms of union and intersection, for the set limits any given sequence (net, general) an arbitrary T 1 space; this representation particular gives a new characterization space.