We investigate commutative semirings, which are formed by a ground set equipped with two binary associative and commutative operations such that one distributes over the other. We narrow down our interest to ideal-simple semirings, that is, semirings without proper ideals. We present the classification of ideal-simple semirings and deal with some classes of ideal-simple semirings, namely semifields and parasemifields. The main result of this thesis is giving tight bounds on the minimal number of generators needed to generate a parasemifield as a semiring. We also study how the semifields that are finitely generated as a semiring look like. Last, but not least, we show that every finitely generated ideal-simple semiring is finitely-generated as a multiplicative semigroup.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:448041 |
| Date | January 2021 |
| Creators | Šíma, Lucien |
| Contributors | Kala, Vítězslav, Korbelář, Miroslav |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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