The existence of congruence-simple semiring S with non-constant multiplication such that 2s = 3t for all s, t ∈ S and S + S = S is proved and hence the most enigmatic class of congruence-simple semirings is not empty.

Today most research related to manufacturing strategy development concentrates on descriptive processes and conceptual models, and therefore lacks the capability of assessing the supportive degree of manufacturing strategy to competitive priorities, and is also difficult to assess the congruence among various decisions of the manufacturing strategy. This paper proposes an approach for manufactu...

An important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic, is that of a filter. Filters can be used, amongst others, to define congruence relations. Specific kinds of filters include Boolean filters and prime filters. In this paper, we define several different filters of residuated lattices and triangle algebras and examine their mutual...

As it was shown in [7], Monoidal t-norm based logic (MTL) is a logic of left-continuous t-norms. In other words, this means that MTL enjoys the standard completeness theorem. In this paper we present a different proof of this theorem. In fact, we prove even more since we show that MTL is complete w.r.t. the class of standard MTL-algebras with finite congruence lattices or equivalently with fini...

Denote by W (T ), r(T ) and ‖T‖ the numerical range, the numerical radius and the spectral norm of a complex matrix T . Let (A,B) be a pair of Hermitian matrices. It is shown that if 0 ∈ W (A+ iB) then d(A,B) = inf{|μ| : μ / ∈ W (A+ iB)} is an upper bound for inf{r(E + iF ) : (A+ E) + i(B + F ) is diagonalizable by congruence}; if 0 / ∈ W (A+ iB) then the Crawford number c(A,B) = min{|μ| : μ ∈ ...

This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals) from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R) is isom...

We shall begin by recalling some material from quadrics1.pdf, which gave the classification of hyperquadrics in R and C up to affine equivalence: CONGRUENCE OR ISOMETRY CLASSIFICATION PROBLEM. Given two affine hyperquadrics Σ1 and Σ2 in R , is there a congruence or isometry T from R to itself mapping Σ1 onto Σ2? There are two possible versions of the question. An arbitrary isometry T from R to ...