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Rings of Multisets and Integer Multinumbers

Author

Listed:
  • Yuriy Chopyuk

    (Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine)

  • Taras Vasylyshyn

    (Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine)

  • Andriy Zagorodnyuk

    (Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine)

Abstract

In the paper, we consider a ring structure on the Cartesian product of two sets of integer multisets. In this way, we introduce a ring of integer multinumbers as a quotient of the Cartesian product with respect to a natural equivalence. We examine the properties of this ring and construct some isomorphisms to subrings of polynomials and Dirichlet series with integer coefficients. In addition, we introduce finite rings of multinumbers “modulo ( p , q ) ” and propose an algorithm for construction of invertible elements in these rings that may be applicable in Public-key Cryptography. An analog of the Little Fermat Theorem for integer multinumbers is proved.

Suggested Citation

  • Yuriy Chopyuk & Taras Vasylyshyn & Andriy Zagorodnyuk, 2022. "Rings of Multisets and Integer Multinumbers," Mathematics, MDPI, vol. 10(5), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:778-:d:760951
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