Description of local multipliers on finite-dimensional associative algebras

Authors

  • Farhodjon Arzikulov V. I. Romanovskiy Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, 9 University Street, Tashkent 100174, Uzbekistan
  • Odiljon Samsaqov Andijan State University, 129 University Street, Andijan 170100, Uzbekistan

Keywords:

associative algebra, left (right) multiplier, derivation, local derivation, local left (right) multiplier

Abstract

In 2020 F. Arzikulov and N. Umrzaqov introduced the concept of a (linear) local multiplier. They proved that every local left (right) multiplier on the matrix ring over a division ring is a left (right, respectively) multiplier. This paper is devoted to (linear) local weak left (right) multipliers on 5-dimensional naturally graded 2-filiform non-split associative algebras. An algorithm for obtaining a common form of the matrices of the weak left (right) multipliers on the 5-dimensional naturally graded 2-filiform non-split associative algebras λ15 and λ25, constructed by I. Karimjanov and M. Ladra, is developed. An algorithm for obtaining a general form of the matrices of the local weak left (right) multipliers on the algebras λ15 and λ25 is also developed. It turns out that the associative algebras λ15 and λ25 have a local weak left (right) multiplier that is not a weak left (right, respectively) multiplier.

Author Biographies

  • Farhodjon Arzikulov, V. I. Romanovskiy Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, 9 University Street, Tashkent 100174, Uzbekistan

    principal researcher

  • Odiljon Samsaqov, Andijan State University, 129 University Street, Andijan 170100, Uzbekistan

    postgraduate student at the department of algebra and analysis, faculty of mathematics

References

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Published

2023-12-28

Issue

No. 3 (2023): Journal of the Belarusian State University. Mathematics and Informatics

Section

Mathematical Logic, Algebra and Number Theory

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How to Cite

[1]
Arzikulov, F. and Samsaqov, O. 2023. Description of local multipliers on finite-dimensional associative algebras. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2023), 32–41.