Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 223-243.

ON PRIME ELEMENTS IN COMMUTATIVE DOMAINS

Boris Širola

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: sirola@math.hr

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.

2020 Mathematics Subject Classification.   13G05, 11R04, 11R09.

Key words and phrases.   Prime element, irreducible element, integral domain, unique factorization domain, quadratic field, ring of integers, order.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/ygjwrc21ly

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