Using the concept of (K,L)-eigenvector, we investigate structure max-min eigenspace associated with a given eigenvalue matrix in algebra (also known as fuzzy algebra). In our approach, is split into several regions according to order relations between and components x. The resulting theory (K,L)-eigenvectors, being based on fundamental results Gondran Minoux, allows describe whole explicitly mo...

We introduce the notion of Boolean measure algebra. It can be described shortly using some standard notations and terminology. If B is any Boolean algebra, let B N denote the algebra of sequences (xn); xn 2 B: Let us write p k 2 B N the sequence such that p k (i) = 1 if i k and p k (i) = 0 if k < i: If x 2 B, denote by x 2 B N the constant sequence x = (x; x; x; : : :): We deene a Boolean measu...

A Heyting algebra is supplemented if each element a has dual pseudo-complement $$a^+$$ , and centrally supplement it central. We show that extension in the same variety of algebras as original. use this tool to investigate new type completion arising context algebraic proof theory, so-called hyper-MacNeille completion. MacNeille its extension. This provides an description algebra, allows develo...

If (Q,n) (R,m) is a surjective local homomorphism with kernel I, such that I ⊆ n and the conormal module I/I has a free summand of rank n, then the degree 2 central subspace of the homotopy Lie algebra of R has dimension greater than or equal to n. This is a corollary of the Main Theorem of this note. The techniques involved provide new proofs of some well known results concerning the conormal ...

X iv :0 81 2. 43 67 v1 [ cs .D M ] 2 3 D ec 2 00 8 ON SOME CLASSES OF FUNCTIONS AND HYPERCUBES DIMITER STOICHKOV KOVACHEV Abstra t. In this paper, some lasses of dis rete fun tions of k-valued logi are onsidered, that depend on sets of their variables in a parti ular way. Obtained results allow to " onstru t" these fun tions and to present them in their tabular, analyti al or matrix form, that ...

i.e., if every fER attains its maximum modulus on C. As a matter of convenience, we shall, in this paper, abbreviate "maximum modulus algebra on K" to "ilf-algebra." Examples of Af-algebras which come to mind immediately are (a) the algebra ft consisting of all functions which are continuous on K and analytic in U, (b) any subalgebra of ft, (c) any algebra (B which is equivalent to an algebra o...

Let g be a Lie algebra over a field k of characteristic zero, and a fix positive integer N. The Lie algebra ĝ = g ⊗k k[t]/t N+1 k[t] is called a truncated current Lie algebra. In this paper a highest-weight theory for ĝ is developed when the underlying Lie algebra g possesses a triangular decomposition. The principal result is the reducibility criterion for the Verma modules of ĝ for a wide cla...