Let p be a polynomial in non-commutative variables x1,x2,…,xn with constant term zero over an algebraically closed field K. The object of study this paper is the image kind algebra upper triangular matrices Tm(K). We introduce family polynomials called multi-index p-inductive for given p. Using we will show that, if identity Tt(K) but not Tt+1(K), then p(Tm(K))⊆Tm(K)(t−1). Equality achieved cas...

This paper provides a lexical entry schema for exclusives covering the adverbs only, just, exclusively, merely, purely, solely, simply, and the adjectives only, sole, pure, exclusive and alone. We argue, on the basis of inter-paraphrasability relations among these exclusives and entailments involving at least and at most, that all of these items make an at-issue contribution of an upper bound o...

Linear constraints occur naturally in many reasoning problems and the information that they represent is often uncertain. There is a difficulty in applying many AI uncertainty formalisms to this situation, as their representation of the underlying logic, either as a mutually exclusive and exhaustive set of possibilities, or with a propositional or a predicate logic, is inappropriate (or at leas...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...