Split absolutely irreducible integer-valued polynomials over discrete valuation domains
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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… read more here.
Keywords: absolutely irreducible; polynomials discrete; integer valued; valued polynomials ... See more keywords
Almost Krull domains and their rings of integer–valued polynomials
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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… read more here.
Keywords: domains rings; almost krull; rings integer; integer valued ... See more keywords
Multiplicative properties of integer valued polynomials over split-quaternions
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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 ). read more here.
Keywords: properties integer; multiplicative properties; polynomials split; integer valued ... See more keywords
Integer-valued polynomials on subsets of upper triangular matrix rings
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DOI: 10.1080/00927872.2024.2316895
Abstract: Abstract S. Frisch, showed that the integer-valued polynomials on upper triangular matrix ring IntTn(K)(Tn(D)):={f∈Tn(K)[x]|f(Tn(D))⊆Tn(D)} is a ring, where D is an integral domain with field of fractions K. Let R1⊆R2 be commutative rings with identity.… read more here.
Keywords: upper triangular; valued polynomials; matrix rings; integer valued ... See more keywords
Integer-valued polynomials satisfying the Lucas property
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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… read more here.
Keywords: integer valued; lucas property; valued polynomials; basis integer ... See more keywords