In this paper, as a result of a theorem of Serre on congruence properties, a complete solution is given for an open question (see the text) presented recently by Kim, Koo and Park. Some further questions and results on similar types of congruence properties of elliptic curves are also presented and discussed.

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

In a previous paper, we started an enumeration of the finitely many levels for which a principal congruence manifold can be a link complement in S. In this paper we give a complete enumeration of all the principal congruence link complements in S, together with their levels in the case when the class number of Q( √ −d) is greater than 1.

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...

This paper defines a probabilistic barbed congruence which turns out to coincide with observational equivalence in a probabilistic extension of CCS. Based on this coincidence result, we provide a sound and complete axiomatisation for the barbed congruence in a finite fragment of probabilistic CCS.

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...

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 generalize the notion of complete binary relation on complete lattice to residuated lattice valued ordered sets and show its properties. Then we focus on complete fuzzy tolerances on fuzzy complete lattices and prove they are in one-to-one correspondence with extensive isotone Galois connections. Finally, we prove that fuzzy complete lattice, factorized by a complete fuzzy tolerance, is agai...