The concept of a combinatorial decomposition of a graded K algebra was introduced by Baclawski-Garsia [4], and they showed that every (finitelygenerated) graded K algebra has such a decomposition. The purpose of this paper is to prove some general properties of combinatorial decompositions, which are useful for finding such decompositions. We then show how to compute combinatorial decomposition...

This paper shows that idempotents in finite rings of integers can act as Generalized Boolean Assignments (GBA’s) by providing a completeness theorem. We introduce the notion of a generic Generalized Boolean Assignment. The mere propagation of such an assignment reveals feasibility (existence of a solution) of a formula in propositional logic. Then, we demystify this general concept by formulati...

Let [Formula: see text] be a set of states physical system. The probabilities the occurrence an event when system is in different define function from to called numerical or, more accurately, text]-probability. Sets text]-probabilities ordered by partial order functions give rise so-called algebras text]-probabilities, particular, ones that are lattice-ordered. Among these, there text]-algebras...

Boolean functions that have constant-degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class ACC. They are also precisely the functions computable efficiently by programs over fixed and finite nilpotent groups. This class is not known to be learnable in any reasonable learning model. In this paper, we provide a deterministic polynomia...

In this paper, we study non-central almost subnormal subgroups of the multiplicative group a division ring satisfying nonzero generalized rational identity. The main result generalizes Chiba’s theorem on subgroups. As an application, get algebraic last has several corollaries which generalize completely or partially some previous results.

This work presents a new framework for Gröbner basis computations with Boolean polynomials. Boolean polynomials can be modelled in a rather simple way, with both coefficients and degree per variable lying in {0, 1}. The ring of Boolean polynomials is, however, not a polynomial ring, but rather the quotient ring of the polynomial ring over the field with two elements modulo the field equations x...