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Sharma, R. K.
- Jordan Regular Generators of General Linear Groups
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Authors
Affiliations
1 Department of Mathematics and Astronomy, Lucknow University, Lucknow, 226007, IN
2 Department of Mathematics, Indian Institute of Technology, Delhi, 110016, IN
1 Department of Mathematics and Astronomy, Lucknow University, Lucknow, 226007, IN
2 Department of Mathematics, Indian Institute of Technology, Delhi, 110016, IN
Source
The Journal of the Indian Mathematical Society, Vol 85, No 3-4 (2018), Pagination: 422-433Abstract
In this article Jordan regular units have been introduced. In particular, it is proved that for n ≥ 2, the general linear group GL(2; F2n) can be generated by Jordan regular units. Further, presentations of GL(2, F4); GL(2, F8); GL(2, F16) and GL(2, F32) have been obtained having Jordan regular units as generators.Keywords
Jordan Regular Units, General Linear Groups.
References
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- Unified Extensions of Strongly Reversible Rings and Links with Other Classic Ring Theoretic Properties
Abstract Views :209 |
PDF Views:1
Authors
Affiliations
1 Indian Institute of Technology, New Delhi-110016, IN
2 Hamdard University, New Delhi 110 062, IN
1 Indian Institute of Technology, New Delhi-110016, IN
2 Hamdard University, New Delhi 110 062, IN
Source
The Journal of the Indian Mathematical Society, Vol 85, No 3-4 (2018), Pagination: 434-448Abstract
Let R be a ring, (M, ≤) a strictly ordered monoid and ω : M → End(R) a monoid homomorphism. The skew generalized power series ring R[[M; ω]] is a compact generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomials rings, (skew) Laurent power series rings, (skew) group rings, (skew) monoid rings, Mal'cev Neumann rings and generalized power series rings. In this paper, we introduce concept of strongly (M, ω)-reversible ring (strongly reversible ring related to skew generalized power series ring R[[M, ω]]) which is a uni ed generalization of strongly reversible ring and study basic properties of strongly (M; ω)-reversible. The Nagata extension of strongly reversible is proved to be strongly reversible if R is Armendariz. Finally, it is proved that strongly reversible ring strictly lies between reduced and reversible ring in the expanded diagram given by Diesl et. al. [7].Keywords
Reduced Ring, Armendariz Ring, Reversible Ring, Linear Armendariz Ring, Symmetric Ring, Duo Ring, Semi-Commutative Ring, Strongly Reversible Ring, Strongly (M; ω)-Reversible Ring.References
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