arXiv subjects

Shohei Izawa

Publications and source records attributed to Shohei Izawa.

3 recordsLinked to original sources

arXiv2014

A "classification" of congruence primal arithmetical algebras

We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove that for a finite algebra, it has an irredundant non-refinable cover consists of primal algebras if and only if it is the both congruence primal and arithmetical. Finally, we obtain combinatorial description of congruence primal arithmetical algebras.

math.LO↗

arXiv2013

Matrix product is many-sorted algebra

It is known that a category of many-sorted algebras on pure sets of similarity type is "concretely equivalent" to a category of single-sorted algebras. In this paper, we characterize a single-sorted variety that corresponds to a many-sorted variety. Such variety is also characterized by the condition that is decomposable with respect to matrix product.

math.LO↗

arXiv2013

Infinitary version of Pol-Inv Galois connection

In this article, we prove infinitary version of one to one correspondence theorem between clones and relational clones on a fixed possibly infinite set. We also characterize the relational clone corresponding to the clone of all finitary operations. By this characterization, we obtain correspondence between finitary clones on a fixed infinite set and relational clones satisfying some condition.

math.LO↗