Original scientific paper

https://doi.org/10.21857/ygjwrc21ly

On prime elements in commutative domains

Boris Širola orcid.org/0000-0003-1000-0808 ; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia

Abstract

We present some results concerning prime elements in integral domains. In particular we deal with the following question: Does every order in an algebraic number field has infinitely many prime elements? Then we show that for real quadratic fields the answer to that question is positive. We also give certain partial results and examples about prime polynomials in two or more variables with coefficients from arbitrary integral domain.

Keywords

Prime element; irreducible element; integral domain; unique factorization domain; quadratic field; ring of integers; order

Hrčak ID:

313632

URI

https://hrcak.srce.hr/313632

Publication date:

24.1.2024.

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