<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Let S be a semiring. An S-semimodule M is called a multiplication semimodule if for each subsemimodule N of M there exists an ideal I of S such that N = IM. In this paper we investigate some properties of multiplication semimodules and generalize some results on multiplication modules to semimodules. We show that every multiplicatively cancellative multiplication semimodule is finitely generated and projective. Moreover, we characterize finitely generated cancellative multiplication S-semimodules when S is a yoked semiring such that every maximal ideal of S is subtractive.</p></abstract>

Let S be a semiring. An S-semimodule M is called a multiplication semimodule if for each subsemimodule N of M there exists an ideal I of S such that N = IM. In this paper we investigate some properties of multiplication semimodules and generalize some results on multiplication modules to semimodules. We show that every multiplicatively cancellative multiplication semimodule is finitely generated and projective. Moreover, we characterize finitely generated cancellative multiplication S-semimodules when S is a yoked semiring such that every maximal ideal of S is subtractive.

Multiplication semimodules

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Multiplication semimodules"}

Let S be a semiring. An S-semimodule M is called a multiplication semimodule if for each subsemimodule N of M there exists an ideal I of S such that N = IM. In...

Multiplication semimodules

Publié en ligne: 17 août 2019

Pages: 172 - 185

Reçu: 08 juin 2016

DOI: https://doi.org/10.2478/ausm-2019-0014

Mots clés
semiring, multiplication semimodule

© 2019 Rafieh Razavi Nazari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Multiplication semimodules

Publié en ligne: 17 août 2019

Pages: 172 - 185

Reçu: 08 juin 2016

DOI: https://doi.org/10.2478/ausm-2019-0014

Mots cléssemiring, multiplication semimodule

© 2019 Rafieh Razavi Nazari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
semiring, multiplication semimodule