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• W3185222521 abstract "In this paper, a semigroup algebra consisting of polynomial expressions with coefficients in a field F and exponents in an additive submonoid M of Q≥0 is called a Puiseux algebra and denoted by F[M]. Here we study the atomic structure of Puiseux algebras. To begin with, we answer the isomorphism problem for the class of Puiseux algebras, that is, we show that for a field F if two Puiseux algebras F[M1] and F[M2] are isomorphic, then the monoids M1 and M2 must be isomorphic. Then we construct three classes of Puiseux algebras satisfying the following well-known atomic properties: the ACCP property, the bounded factorization property, and the finite factorization property. We show that there are bounded factorization Puiseux algebras with extremal systems of sets of lengths, which allows us to prove that Puiseux algebras cannot be determined (up to isomorphism) by their arithmetic of lengths. Finally, we give a full description of the seminormal closure, root closure, and complete integral closure of a Puiseux algebra, and we use this description to provide a class of antimatter Puiseux algebras (i.e., Puiseux algebras containing no irreducibles)." @default.
• W3185222521 created "2021-08-02" @default.
• W3185222521 creator A5066438959 @default.
• W3185222521 date "2021-07-15" @default.
• W3185222521 modified "2023-09-27" @default.
• W3185222521 title "On semigroup algebras with rational exponents" @default.
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• W3185222521 doi "https://doi.org/10.1080/00927872.2021.1949018" @default.
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