this paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical galois theory and involves generalized central extensions, commutators, and internal groupoids in barr exact mal’tsev and more general categories. galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

Abstract The main aim of this article is to study admissible congruences on a type B semigroup. First, we give characterizations the minimum congruence whose trace normal After obtaining some properties with same semigroup, introduce notion subsemigroup and maximum kernels are subsemigroups. Finally, concept pair semigroup given, two associated obtained.

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated...

Worldwide, the determination of coordinates from a Global Navigation Satellite System (GNSS) survey (in Network Real Time Kinematic, Precise Point Positioning, or static mode) has been analysed in several scientific and technical applications. Many those have carried out to compare Positioning (PPP), Kinematic (NRTK), modes’ solutions, usually, using latter as true most plausible solution. This...

Concurrent ML is an extension of Standard ML with π-calculus-like primitives for multi-threaded programming. CML has a reduction semantics, but to date there has been no labelled transitions semantics provided for the entire language. In this paper, we present a labelled transition semantics for a fragment of CML called μνCML which includes features not covered before: dynamically generated loc...