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Published in 2022 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2022.03.006
Abstract: Regarding non-unique factorization of integer-valued polynomials over a discrete valuation domain (R, M) with finite residue field, it is known that there exist absolutely irreducible elements, that is, irreducible elements all of whose powers factor…
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Keywords:
absolutely irreducible;
polynomials discrete;
integer valued;
valued polynomials ... See more keywords
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Published in 2020 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2019.106269
Abstract: Abstract We investigate some ring theoretic properties of almost Krull domains. By using the language of star operations, we shed new light on the work of Pirtle on almost Krull domains. That allows us to…
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Keywords:
domains rings;
almost krull;
rings integer;
integer valued ... See more keywords
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Published in 2020 at "Communications in Algebra"
DOI: 10.1080/00927872.2020.1834572
Abstract: Abstract We study localization properties and the prime spectrum of the integer-valued polynomial ring where (respectively ) is the algebra of split-quaternion over ℤ (respectively over ).
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Keywords:
properties integer;
multiplicative properties;
polynomials split;
integer valued ... See more keywords
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Published in 2021 at "Turkish Journal of Mathematics"
DOI: 10.3906/mat-2102-104
Abstract: The classical theorem of Lucas states that the binomial polynomials, which form a basis for integer-valued polynomials, satisfy a congruence relation related to their integer parameters. We consider here three problems connected with this result…
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Keywords:
integer valued;
lucas property;
valued polynomials;
basis integer ... See more keywords