It is known that commutative BCK-algebras form a variety, but BCK-algebras do not [4]. Therefore H. Yutani introduced the notion of quasicommutative BCK-algebras. In this article we first present the notion and general theory of quasi-commutative BCI-algebras. Then we discuss the reduction of the type of quasi-commutative BCK-algebras and some special classes of quasicommutative BCI-algebras.

Under certain hypotheses, diffusion semigroups on commutative L-spaces are known to have an analytic extension for | arg z| < π 2 − arctan |p−2| 2 √ p−1 . In this paper it is shown that semigroups on non-commutative L-spaces have the same extension under suitable conditions. These conditions even lead to a new result in the commutative case. Further, some examples are considered.

We demonstrate that deciding if two terms containing otherwise uninter-preted associative, commutative, and associative-commutative function symbols and commutative variable-binding operators are equal is polynomially equivalent to determining if two graphs are isomorphic. The reductions we use provide insight into this result and suggest polynomial time special cases.

In this paper solutions to three open problems on ordered commutative monoids posed in [4] are presented. By an ordered monoid we always mean a totally ordered monoid. All the problems are related to the class of ordered commutative monoids which are homomorphic images of ordered free commutative monoids.

Atomic objects have suitable properties to realize reliable distributed computing. Using semantic information of atomic objects can make reliable distributed computing highly concurrent. This paper describes a commutativity based concurrency control algorithm in a multiversion object for highly concurrent distributed computing. Weihl proposed two concurrency control algorithms based on a commut...

In this note, we show that any epimorphism originating at a von Neumann regular ring (not necessary commutative) is universal localization. As an application, prove the Telescope Conjecture holds for unbounded derived categories of rings commutative).

*Correspondence: [email protected] 1Edward L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA 2CNRS, Laboratoire des signaux et systèmes (L2S) CentraleSupélec, 3 rue Joliot-Curie, Gif-sur-Yvette, 91192, France Full list of author information is available at the end of the article Abstract The purpose of this paper is to study the problem of generalizing the Belavkin-Kal...

Spider diagrams provide a visual logic to express relations between sets and their elements, extending the expressiveness of Venn diagrams. Sound and complete inference systems for spider diagrams have been developed and it is known that they are equivalent in expressive power to monadic first-order logic with equality, MFOL[1⁄4]. languages that are finite unions of languages of the form K G , ...