Results 271 to 280 of about 665,695 (311)
Some of the next articles are maybe not open access.
Journal of Group Theory, 2003
Summary: For a vector space \(V\) over the division ring \(D\), let \(\text{FEnd}_D(V)\) be the set of all \(D\)-transformations \(x\in\text{End}_D(V)\) such that \(x\) has finite rank, and let \(\text{FGL}_D(V)\) be the set of all \(g\in\text{GL}_D(V)\) such that \(g-1\) has finite rank.
Phillips, Richard E., Wald, Jeanne
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Summary: For a vector space \(V\) over the division ring \(D\), let \(\text{FEnd}_D(V)\) be the set of all \(D\)-transformations \(x\in\text{End}_D(V)\) such that \(x\) has finite rank, and let \(\text{FGL}_D(V)\) be the set of all \(g\in\text{GL}_D(V)\) such that \(g-1\) has finite rank.
Phillips, Richard E., Wald, Jeanne
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Journal of Algebra and Its Applications, 2014
A ring with involution * is called *-clean if each of its elements is the sum of a unit and a projection. Clearly a *-clean ring is clean. Vaš asked whether there exists a clean ring with involution * that is not *-clean. In a recent paper, Gao, Chen and the first author investigated when a group ring RG with classical involution * is *-clean and ...
Li, Yuanlin +2 more
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A ring with involution * is called *-clean if each of its elements is the sum of a unit and a projection. Clearly a *-clean ring is clean. Vaš asked whether there exists a clean ring with involution * that is not *-clean. In a recent paper, Gao, Chen and the first author investigated when a group ring RG with classical involution * is *-clean and ...
Li, Yuanlin +2 more
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Algebra Colloquium, 2011
It is shown that if the group ring RQ8 of the quaternion group Q8 of order 8 over an integral domain R is duo, then R is a field for the following cases: (1) char R ≠ 0, and (2) char R = 0 and S ⊆ R ⊆ KS, where S is a ring of algebraic integers and KS is its quotient field.
Gao, Weidong, Li, Yuanlin
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It is shown that if the group ring RQ8 of the quaternion group Q8 of order 8 over an integral domain R is duo, then R is a field for the following cases: (1) char R ≠ 0, and (2) char R = 0 and S ⊆ R ⊆ KS, where S is a ring of algebraic integers and KS is its quotient field.
Gao, Weidong, Li, Yuanlin
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2015
This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra.
Jespers, Eric, Del Rio Mateos, Angel
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This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra.
Jespers, Eric, Del Rio Mateos, Angel
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Journal of Algebra and Its Applications, 2009
In this paper we characterize *-prime group rings. We prove that the group ring RG of the group G over the ring R is *-prime if and only if R is *-prime and Λ+(G) = (1). In the process we obtain more examples of group rings which are *-prime but not strongly prime.
Joshi, Kanchan +2 more
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In this paper we characterize *-prime group rings. We prove that the group ring RG of the group G over the ring R is *-prime if and only if R is *-prime and Λ+(G) = (1). In the process we obtain more examples of group rings which are *-prime but not strongly prime.
Joshi, Kanchan +2 more
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Canadian Mathematical Bulletin, 1975
Let R and S be rings with 1, G a group and RG and SG the corresponding group rings. In this paper, we study the problem of when RG≃SG implies R≃S. This problem was previously investigated in [8] for the case where G is assumed to be infinite cyclic.
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Let R and S be rings with 1, G a group and RG and SG the corresponding group rings. In this paper, we study the problem of when RG≃SG implies R≃S. This problem was previously investigated in [8] for the case where G is assumed to be infinite cyclic.
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Canadian Mathematical Bulletin, 1972
The purpose of this note is to generalize a result of Gulliksen, Ribenboim and Viswanathan which characterized local group rings when both the ring and the group are commutative.We assume throughout that all rings are associative with identity. If R is a ring we call R local if R/J(R) is a division ring where J(R) denotes the Jacobson radical of R.
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The purpose of this note is to generalize a result of Gulliksen, Ribenboim and Viswanathan which characterized local group rings when both the ring and the group are commutative.We assume throughout that all rings are associative with identity. If R is a ring we call R local if R/J(R) is a division ring where J(R) denotes the Jacobson radical of R.
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Catalytic Enantioselective Ring-Opening Reactions of Cyclopropanes
Chemical Reviews, 2021Vincent Pirenne +2 more
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C–C Bond Cleavages of Cyclopropenes: Operating for Selective Ring-Opening Reactions
Chemical Reviews, 2021Ruben Vicente
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