Results 241 to 250 of about 2,156,473 (283)
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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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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 Journal of Mathematics, 1970
Let R be a commutative ring with unity and let G be a group. The group ring RG is a free R-module having the elements of G as a basis, with multiplication induced byThe first theorem in this paper deals with idempotents in RG and improves a result of Connell.
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Let R be a commutative ring with unity and let G be a group. The group ring RG is a free R-module having the elements of G as a basis, with multiplication induced byThe first theorem in this paper deals with idempotents in RG and improves a result of Connell.
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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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Canadian Journal of Mathematics, 1973
Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has been solved for char K = 0 in [1] and for char K = p > 0 in [3]. The answer is as follows.
Passi, I. B. S. +2 more
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Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has been solved for char K = 0 in [1] and for char K = p > 0 in [3]. The answer is as follows.
Passi, I. B. S. +2 more
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Iranian Journal of Science and Technology, Transactions A: Science, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ashrafi, Nahid, Nasibi, Ebrahim
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ashrafi, Nahid, Nasibi, Ebrahim
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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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Rings of Quotients of Group Rings
Canadian Journal of Mathematics, 1969The group ring AG of a group G and a ring A is the ring of all formal sums Σg∈G agg with ag ∈ A and with only finitely many non-zero ag. Elements of A are assumed to commute with the elements of G. In (2), Connell characterized or completed the characterization of Artinian, completely reducible and (von Neumann) regular group rings ((2) also contains ...
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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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