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Article

Supersymmetric Polynomials and a Ring of Multisets of a Banach Algebra

by
Iryna Chernega
1 and
Andriy Zagorodnyuk
2,*
1
Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3b, Naukova Str., 79060 Lviv, Ukraine
2
Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(10), 511; https://doi.org/10.3390/axioms11100511
Submission received: 31 July 2022 / Revised: 24 September 2022 / Accepted: 25 September 2022 / Published: 27 September 2022
(This article belongs to the Special Issue Approximation Theory and Related Applications)
Versions Notes

Abstract

In this paper, we consider rings of multisets consisting of elements of a Banach algebra. We investigate the algebraic and topological structures of such rings and the properties of their homomorphisms. The rings of multisets arise as natural domains of supersymmetric functions. We introduce a complete metrizable topology on a given ring of multisets and extend some known results about structures of the rings to the general case. In addition, we consider supersymmetric polynomials and other supersymmetric functions related to these rings. This paper contains a number of examples and some discussions.
Keywords: set of multisets; topological rings; supersymmetric polynomials; symmetric bases set of multisets; topological rings; supersymmetric polynomials; symmetric bases

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MDPI and ACS Style

Chernega, I.; Zagorodnyuk, A. Supersymmetric Polynomials and a Ring of Multisets of a Banach Algebra. Axioms 2022, 11, 511. https://doi.org/10.3390/axioms11100511

AMA Style

Chernega I, Zagorodnyuk A. Supersymmetric Polynomials and a Ring of Multisets of a Banach Algebra. Axioms. 2022; 11(10):511. https://doi.org/10.3390/axioms11100511

Chicago/Turabian Style

Chernega, Iryna, and Andriy Zagorodnyuk. 2022. "Supersymmetric Polynomials and a Ring of Multisets of a Banach Algebra" Axioms 11, no. 10: 511. https://doi.org/10.3390/axioms11100511

APA Style

Chernega, I., & Zagorodnyuk, A. (2022). Supersymmetric Polynomials and a Ring of Multisets of a Banach Algebra. Axioms, 11(10), 511. https://doi.org/10.3390/axioms11100511

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