Homogeneity of zero-divisors, units and idempotents in a graded ring
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913943653449728 |
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| author | Tarizadeh, Abolfazl |
| author_facet | Tarizadeh, Abolfazl |
| contents | In this article we prove several important results on graded rings, especially monoid-rings, that are motivated and inspired by Kaplansky's zero-divisor, unit and idempotents conjectures. Among the main results, we first generalize Kaplansky's zero-divisor conjecture of group-rings $K[G]$ (with $K$ a field) to the more general setting of $G$-graded rings $R=\bigoplus\limits_{n\in G}R_{n}$ with $G$ a torsion-free group. Then we prove that ... |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02880 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homogeneity of zero-divisors, units and idempotents in a graded ring Tarizadeh, Abolfazl Commutative Algebra Algebraic Geometry Group Theory Rings and Algebras 13A02, 16S34, 13A15, 20K15, 20K20, 14A05 In this article we prove several important results on graded rings, especially monoid-rings, that are motivated and inspired by Kaplansky's zero-divisor, unit and idempotents conjectures. Among the main results, we first generalize Kaplansky's zero-divisor conjecture of group-rings $K[G]$ (with $K$ a field) to the more general setting of $G$-graded rings $R=\bigoplus\limits_{n\in G}R_{n}$ with $G$ a torsion-free group. Then we prove that ... |
| title | Homogeneity of zero-divisors, units and idempotents in a graded ring |
| topic | Commutative Algebra Algebraic Geometry Group Theory Rings and Algebras 13A02, 16S34, 13A15, 20K15, 20K20, 14A05 |
| url | https://arxiv.org/abs/2309.02880 |