arXiv subjects

Janusz Zieliński

Publications and source records attributed to Janusz Zieliński.

5 recordsLinked to original sources

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

An approach to the Jacobian Conjecture in terms of irreducibility

We present some motivations and discuss various aspects of an approach to the Jacobian Conjecture in terms of irreducible elements and square-free elements.

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↗

arXiv2016

Analogs of Jacobian conditions for subrings

We present a generalization of the Jacobian Conjecture for m polynomials in n variables: f1,...,fm belonging to k[x1,...,xn], where k is a field of characteristic zero and m=1,...,n. We express the generalized Jacobian condition in terms of irreducible and square-free elements of the subalgebra k[f1,...,fm]. We also discuss obtained properties in a more general setting - for subrings of unique factorization domains.

math.AC↗