Semihyperrings Characterized by Their Hyperideals
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arXiv
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| Natura: | Preprint |
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2010
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| _version_ | 1866910786220195840 |
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| author | Shabir, M. Mehmood, Nayyar Corsini, Piergiulio |
| author_facet | Shabir, M. Mehmood, Nayyar Corsini, Piergiulio |
| contents | The concept of hypergroup is generalization of group, first was introduced by Marty [9]. This theory had applications to several domains. Marty had applied them to groups, algebraic functions and rational functions. M. Krasner has studied the notion of hyperring in [11]. G.G Massouros and C.G Massouros defined hyperringoids and apply them in generalization of rings in [10]. They also defined fortified hypergroups as a generalization of divisibility in algebraic structures and use them in Automata and Language theory. T. Vougiouklis has defined the representations and fundamental relations in hyperrings in [14, 15]. R. Ameri, H. Hedayati defined k-hyperideals in semihyperrings in [2]. B. Davvaz has defined some relations in hyperrings and prove Isomorphism theorems in [7]. The aim of this article is to initiate the study of semihyperrings and characterize it with hyperideals. In this article we defined semihyperrings, hyperideals, prime, semiprime, irreducible, strongly irreducible hyperideals, m-systems, p-systems, i-systems and regular semihyperrings. We also shown that the lattice of irreducible hyperideals of semihyperring R admits the structure of topology, which is called irreducible spectrum topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1008_3448 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Semihyperrings Characterized by Their Hyperideals Shabir, M. Mehmood, Nayyar Corsini, Piergiulio Group Theory The concept of hypergroup is generalization of group, first was introduced by Marty [9]. This theory had applications to several domains. Marty had applied them to groups, algebraic functions and rational functions. M. Krasner has studied the notion of hyperring in [11]. G.G Massouros and C.G Massouros defined hyperringoids and apply them in generalization of rings in [10]. They also defined fortified hypergroups as a generalization of divisibility in algebraic structures and use them in Automata and Language theory. T. Vougiouklis has defined the representations and fundamental relations in hyperrings in [14, 15]. R. Ameri, H. Hedayati defined k-hyperideals in semihyperrings in [2]. B. Davvaz has defined some relations in hyperrings and prove Isomorphism theorems in [7]. The aim of this article is to initiate the study of semihyperrings and characterize it with hyperideals. In this article we defined semihyperrings, hyperideals, prime, semiprime, irreducible, strongly irreducible hyperideals, m-systems, p-systems, i-systems and regular semihyperrings. We also shown that the lattice of irreducible hyperideals of semihyperring R admits the structure of topology, which is called irreducible spectrum topology. |
| title | Semihyperrings Characterized by Their Hyperideals |
| topic | Group Theory |
| url | https://arxiv.org/abs/1008.3448 |