7 citations · 14 across the 9 of their papers we have counts for
9 papers
A polynomial composites
Lukasz Matysiak
Polynomial composites were introduced by Anderson, Anderson, and Zafrullah. In this paper we study many different algebraic properties of polynomial composites like ACCP, atomic, S…
On square-free and radical factorizations and existence of some divisors
Lukasz Matysiak
We discuss various square-free and radical factorizations and existence of some divisors in monoids in the context of: atomicity, ascending chain condition for principal ideals, a…
A polynomial composites and monoid domains as algebraic structures and their applications
Magdalena Jankowska, Lukasz Matysiak
This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domain…
Matrices of infinite dimensions and their applications
Lukasz Matysiak, Weronika Przewozniak, Natalia Rulinska
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study.…
K + M constructions with general overrings and relationships with polynomial composites
Lukasz Matysiak
In this paper we consider the construction of K + M, where K is the domain, M is the maximal ideal of a some ring of polynomials with coefficients from the field L, where K is its…
Polynomial composites and certain types of fields extensions
Łukasz Matysiak
In this paper I consider polynomial composites with the coefficients from . We already know many properties, but we do not know the answer to the question of whether th…
On properties of composites and monoid domains
Lukasz Matysiak
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I star…
A note on square-free factorizations
Piotr Jędrzejewicz, Łukasz Matysiak, Janusz Zieliński
We analyze properties of various square-free factorizations in greatest common divisor domains and domains satisfying the ascending chain condition for principal ideals.
On some factorial properties of subrings
Piotr Jędrzejewicz, Łukasz Matysiak, Janusz Zieliński
We discuss various factorial properties of subrings as well as properties involving irreducible and square-free elements, in particular ones connected with Jacobian conditions.