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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The prime spectrum of an $L$-algebra
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by Wolfgang Rump and Leandro Vendramin;
Proc. Amer. Math. Soc. 152 (2024), 3197-3207
DOI: https://doi.org/10.1090/proc/16802
Published electronically: June 5, 2024

Abstract:

We prove that the lattice of ideals of an arbitrary $L$-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of $L$-algebras and characterize prime ideals in topological terms.
References
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Bibliographic Information
  • Wolfgang Rump
  • Affiliation: Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
  • MR Author ID: 226306
  • Email: rump@mathematik.uni-stuttgart.de
  • Leandro Vendramin
  • Affiliation: Department of Mathematics and Data Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel
  • MR Author ID: 829575
  • ORCID: 0000-0003-0954-7785
  • Email: Leandro.Vendramin@vub.be
  • Received by editor(s): June 2, 2022
  • Received by editor(s) in revised form: January 8, 2024
  • Published electronically: June 5, 2024
  • Additional Notes: The second author was supported in part by OZR3762 of Vrije Universiteit Brussel and FWO Senior Research Project G004124N

  • Dedicated: to B. V. M.
  • Communicated by: Jerzy Weyman
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3197-3207
  • MSC (2020): Primary 06B10, 06F05, 08A55
  • DOI: https://doi.org/10.1090/proc/16802
  • MathSciNet review: 4767255