Journal: Journal of Algebra and Its Applications

Abbreviation

J. Algebr. Appl.

Publisher

World Scientific

Journal Volumes

ISSN

0219-4988
1793-6829

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2013 - 201922020 - 20241
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Publications 1 - 3 of 3
  • Polyfunctions over commutative rings
    Item type: Journal Article
    Specker, Ernst; Hungerbühler, Norbert; Wasem, Micha (2024)
    Journal of Algebra and Its Applications
    A function f : R -> R, where R is a commutative ring with unit element, is called polyfunction if it admits a polynomial representative p is an element of R[x]. Based on this notion, we introduce ring invariants which associate to R the numbers s(R) and s(R '; R), where R ' is the subring generated by 1. For the ring R = Zeta/n Zeta the invariant s(R) coincides with the number theoretic Smarandache or Kempner function s(n). If every function in a ring R is a polyfunction, then R is a finite field according to the Redei-Szele theorem, and it holds that s(R) = |R|. However, the condition s(R) = |R| does not imply that every function f : R -> R is a polyfunction. We classify all finite commutative rings R with unit element which satisfy s(R) = |R|. For infinite rings R, we obtain a bound on the cardinality of the subring R ' and for s(R '; R) in terms of s(R). In particular we show that |R '|<= s(R)!. We also give two new proofs for the Redei-Szele theorem which are based on our results.
  • Repetitive higher cluster categories of type An
    Item type: Journal Article
    Lamberti, Lisa (2014)
    Journal of Algebra and Its Applications
    We show that the repetitive higher cluster category of type An, defined as the orbit category Db(mod kAn)/(τ−1[m])p, is equivalent to a category defined on a subset of diagonals in a regular polygon. This generalizes the construction of Caldero–Chapoton–Schiffler [Quivers with relations arising from clusters (Ancase), Trans. Amer. Math.Soc. 358(3) (2006) 1347–1364], which we recover when p = m =1,and the work of Baur–Marsh, [A geometric description of the m-cluster categories, Trans. Amer. Math.Soc. 360(11) (2008) 5789–5803], treating the case p =1,m>1. Our approach also leads to a geometric model of the bounded derived category in type A.
  • Graded cartan matrices of defect 2 blocks of symmetric groups
    Item type: Journal Article
    Bogdanic, Dusko (2013)
    Journal of Algebra and Its Applications
Publications 1 - 3 of 3