arXiv subjects

Łukasz Matysiak

Publications and source records attributed to Łukasz Matysiak.

4 recordsLinked to original sources

arXiv2021

Polynomial composites and certain types of fields extensions

In this paper I consider polynomial composites with the coefficients from $K\subset L$. We already know many properties, but we do not know the answer to the question of whether there is a relationship between composites and field extensions. I present the characterization of some known field extensions in terms of polynomial composites. This paper contains the opening problem of characterization of ideals in polynomial composites with respect to various field extensions. I also present the full possible characterization of certain field extensions.

math.AC↗

arXiv2018

On properties of square-free elements in commutative cancellative monoids

We discuss various square-free factorizations in monoids in the context of: atomicity, ascending chain condition for principal ideals, decomposition, and a greatest common divisor property. Moreover, we obtain a full characterization of submonoids of factorial monoids in which all square-free elements of a submonoid are square-free in a monoid. We also present factorial properties implying that all atoms of a submonoid are square-free in a monoid.

math.AC↗

arXiv2016

A note on square-free factorizations

We analyze properties of various square-free factorizations in greatest common divisor domains and domains satisfying the ascending chain condition for principal ideals.

math.AC↗

arXiv2016

On some factorial properties of subrings

We discuss various factorial properties of subrings as well as properties involving irreducible and square-free elements, in particular ones connected with Jacobian conditions.

math.AC↗