Startseite Mathematik Ultramatricial algebras over commutative chain semirings and application to MV-algebras
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Ultramatricial algebras over commutative chain semirings and application to MV-algebras

  • Antonio Di Nola EMAIL logo , Giacomo Lenzi und Tran Giang Nam
Veröffentlicht/Copyright: 27. Oktober 2019
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 32 Heft 2

Abstract

In this paper, we give a complete description of strongly projective semimodules over a semiring which is a finite direct product of matrix semirings over commutative chain semirings. We then classify ultramatricial algebras over commutative chain semirings by their ordered SK0-groups. Consequently, we get that there is a one-one correspondence between isomorphism classes of ultramatricial algebras A whose SK0⁢(A) is lattice-ordered over a given commutative chain semiring and isomorphism classes of countable MV-algebras.

Keywords: Strongly projective semimodule; ultramatricial algebras over semirings; MV-algebras
MSC 2010: 16Y60; 06D35; 16E20; 18G05

Communicated by Manfred Droste

Funding statement: The third author is partially supported by Vietnam Ministry of Education and Training under the grant number B2018.SPD.02.

Acknowledgements

This work was carried out during the third author’s visit to the University of Salerno. He would like to thank the Department of Mathematics for hospitality. Also, the authors take an opportunity to express their deep gratitude to the anonymous referee for extremely careful reading, highly professional working with our manuscript, and valuable suggestions. Finally, we would like to thank the editor for his suggestion making us aware of the reference [10] which provides an interesting connection between semirings and weighted automata theory.

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Received: 2019-02-27
Revised: 2019-09-20
Published Online: 2019-10-27
Published in Print: 2020-03-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Operational rules and generalized special polynomials
  3. Linearity of some low-complexity mapping class groups
  4. Ultramatricial algebras over commutative chain semirings and application to MV-algebras
  5. On a group analogue of the Heyde theorem
  6. Explicit presentation of an Iwasawa algebra: The case of pro-p Iwahori subgroup of SLn(ℤp)
  7. Generalized Riesz potentials of functions in Morrey spaces L(1,ϕ;κ)(G) over non-doubling measure spaces
  8. On rough singular integrals along real-analytic submanifolds
  9. Dimension-free estimates for the vector-valued variational operators
  10. Upper bound of multiplicity in prime characteristic
  11. Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients
  12. Irreducible and permutative representations of ultragraph Leavitt path algebras
  13. Twisted tensor products of φ-coordinated modules for nonlocal vertex algebras
  14. Explicit decomposition theorem for special Schubert varieties
  15. On the Hirzebruch–Kobayashi–Ono proportionality principle and the non-existence of compact solvable Clifford–Klein forms of certain homogeneous spaces
  16. The Lie group of vertical bisections of a regular Lie groupoid
  17. Chain conditions for graph C*-algebras
  18. Congruences in Hermitian Jacobi and Hermitian modular forms
  19. The Jensen–Pólya program for various L-functions
https://doi.org/10.1515/forum-2019-0056
Schlagwörter für diesen Artikel
Strongly projective semimodule; ultramatricial algebras over semirings; MV-algebras

Artikel in diesem Heft

  1. Frontmatter
  2. Operational rules and generalized special polynomials
  3. Linearity of some low-complexity mapping class groups
  4. Ultramatricial algebras over commutative chain semirings and application to MV-algebras
  5. On a group analogue of the Heyde theorem
  6. Explicit presentation of an Iwasawa algebra: The case of pro-p Iwahori subgroup of SLn(ℤp)
  7. Generalized Riesz potentials of functions in Morrey spaces L(1,ϕ;κ)(G) over non-doubling measure spaces
  8. On rough singular integrals along real-analytic submanifolds
  9. Dimension-free estimates for the vector-valued variational operators
  10. Upper bound of multiplicity in prime characteristic
  11. Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients
  12. Irreducible and permutative representations of ultragraph Leavitt path algebras
  13. Twisted tensor products of φ-coordinated modules for nonlocal vertex algebras
  14. Explicit decomposition theorem for special Schubert varieties
  15. On the Hirzebruch–Kobayashi–Ono proportionality principle and the non-existence of compact solvable Clifford–Klein forms of certain homogeneous spaces
  16. The Lie group of vertical bisections of a regular Lie groupoid
  17. Chain conditions for graph C*-algebras
  18. Congruences in Hermitian Jacobi and Hermitian modular forms
  19. The Jensen–Pólya program for various L-functions
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