Minus Partial Order in Regular Modules
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866911886313783296 |
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| author | Ungor, Burcu Halicioglu, Sait Harmanci, Abdullah Marovt, Janko |
| author_facet | Ungor, Burcu Halicioglu, Sait Harmanci, Abdullah Marovt, Janko |
| contents | The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied on Rickart rings. In this paper, we extend the concept of the minus relation to the module theoretic setting and prove that this relation is a partial order when the module is regular. Moreover, various characterizations of the minus partial order in regular modules are presented and some well-known results are also generalized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_02119 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Minus Partial Order in Regular Modules Ungor, Burcu Halicioglu, Sait Harmanci, Abdullah Marovt, Janko Rings and Algebras 06A06, 06F25, 06F99, 16B99 The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied on Rickart rings. In this paper, we extend the concept of the minus relation to the module theoretic setting and prove that this relation is a partial order when the module is regular. Moreover, various characterizations of the minus partial order in regular modules are presented and some well-known results are also generalized. |
| title | Minus Partial Order in Regular Modules |
| topic | Rings and Algebras 06A06, 06F25, 06F99, 16B99 |
| url | https://arxiv.org/abs/1907.02119 |