On the genus of the k-maximal hypergraph of commutative rings
| Autor: | K. Selvakumar, V. C. Amritha |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Vertex (graph theory)
Hypergraph Computer Science::Information Retrieval 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 0102 computer and information sciences Commutative ring 01 natural sciences Combinatorics TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES 010201 computation theory & mathematics ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::General Literature Discrete Mathematics and Combinatorics 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Discrete Mathematics, Algorithms and Applications. 11:1950010 |
| ISSN: | 1793-8317 1793-8309 |
| Popis: | Let [Formula: see text] be a commutative ring with identity and [Formula: see text], a fixed integer. Let [Formula: see text] be the set of all [Formula: see text]-maximal elements in [Formula: see text] Associate a [Formula: see text]-maximal hypergraph [Formula: see text] to [Formula: see text] with vertex set [Formula: see text] and for distinct elements [Formula: see text] in [Formula: see text], the set [Formula: see text] is an edge of [Formula: see text] if and only if [Formula: see text] and [Formula: see text] for all [Formula: see text]. In this paper, we determine all isomorphism classes of finite commutative non-local rings with identity whose [Formula: see text]-maximal hypergraph has genus one. Finally, we classify all finite commutative non-local rings [Formula: see text] for which [Formula: see text] is projective. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|