Making use of its smooth structure only, out a connected oriented $4$-manifold von Neumann algebra is constructed. As special four dimensional phenomenon this approximated by algebraic (i.e., formal) curvature tensors the underlying and itself hyperfinite factor ${\rm II}_1$ type hence unique up to abstract isomorphisms algebras. Nevertheless over fixed admits representation on Hilbert space su...

This article, aimed specifically at young mathematical logicians, gives a gentle introduction to some of the central achievements and problems of universal algebra during the last 25 years. I intend in this article to introduce nonspecialists to the fact that there are deep results in contemporary universal algebra. The first four sections give the context in which universal algebra has somethi...

In this paper, we define the Gröbner-Shirshov bases for a dialgebra. The composition-diamond lemma for dialgebras is given then. As a result, we obtain a Gröbner-Shirshov basis for the universal enveloping algebra of a Leibniz algebra.

In this paper, by using Gröbner–Shirshov bases for non-associative algebras invented by A. I. Shirshov in 1962, we show I. P. Shestakov’s result that any Akivis algebra can be embedded into its universal enveloping algebra.

The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular problem was not implemented in standard software packages like REDUCE, MATHEMATICA, etc. and if the using of internal programming languages of the packages look...