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 this paper we investigate some properties of multiplication semimodules and generalize some results on multiplication modules to semimodules...
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Sciendo
2019-08-01
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| Series: | Acta Universitatis Sapientiae: Mathematica |
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| Online Access: | https://doi.org/10.2478/ausm-2019-0014 |
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doaj-17c66449fc374950bec05907dcc81b822021-09-06T19:41:26ZengSciendoActa Universitatis Sapientiae: Mathematica2066-77522019-08-0111117218510.2478/ausm-2019-0014ausm-2019-0014Multiplication semimodulesNazari Rafieh Razavi0Ghalandarzadeh Shaban1Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, IranFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, IranLet 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.https://doi.org/10.2478/ausm-2019-0014semiringmultiplication semimodule16y60 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nazari Rafieh Razavi Ghalandarzadeh Shaban |
| spellingShingle |
Nazari Rafieh Razavi Ghalandarzadeh Shaban Multiplication semimodules Acta Universitatis Sapientiae: Mathematica semiring multiplication semimodule 16y60 |
| author_facet |
Nazari Rafieh Razavi Ghalandarzadeh Shaban |
| author_sort |
Nazari Rafieh Razavi |
| title |
Multiplication semimodules |
| title_short |
Multiplication semimodules |
| title_full |
Multiplication semimodules |
| title_fullStr |
Multiplication semimodules |
| title_full_unstemmed |
Multiplication semimodules |
| title_sort |
multiplication semimodules |
| publisher |
Sciendo |
| series |
Acta Universitatis Sapientiae: Mathematica |
| issn |
2066-7752 |
| publishDate |
2019-08-01 |
| description |
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. |
| topic |
semiring multiplication semimodule 16y60 |
| url |
https://doi.org/10.2478/ausm-2019-0014 |
| work_keys_str_mv |
AT nazarirafiehrazavi multiplicationsemimodules AT ghalandarzadehshaban multiplicationsemimodules |
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1717766194615812096 |