Results 231 to 240 of about 219,014 (266)
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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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Canadian Journal of Mathematics, 1963
LetRbe the discrete group ring of the groupGover the ringA. In this paper we attempt to find necessary and sufficient conditions onGandAso thatRwill have some standard ring-theoretic property ; among the properties considered are those of being artinian, regular, self-injective, and semi-prime.The contents of this paper form essentially the author's ...
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LetRbe the discrete group ring of the groupGover the ringA. In this paper we attempt to find necessary and sufficient conditions onGandAso thatRwill have some standard ring-theoretic property ; among the properties considered are those of being artinian, regular, self-injective, and semi-prime.The contents of this paper form essentially the author's ...
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Periodica Mathematica Hungarica, 2021
If \(R\) is a ring and \(G\) is a group, the author proves that every finitely generated left module over the group ring \(RG\) can be embedded into some free left \(RG\)-module if and only if \(G\) is finite and every finitely generated left module over the ring \(R\) can be embedded into some free left \(R\)-module.
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If \(R\) is a ring and \(G\) is a group, the author proves that every finitely generated left module over the group ring \(RG\) can be embedded into some free left \(RG\)-module if and only if \(G\) is finite and every finitely generated left module over the ring \(R\) can be embedded into some free left \(R\)-module.
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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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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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2012 IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications, 2012
In many applications of group signatures, not only a signer's identity but also which group the signer belongs to is sensitive information regarding signer privacy. In this paper, we study these applications and combine a group signature with a ring signature to create a ring group signature, which specifies a set of possible groups without revealing ...
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In many applications of group signatures, not only a signer's identity but also which group the signer belongs to is sensitive information regarding signer privacy. In this paper, we study these applications and combine a group signature with a ring signature to create a ring group signature, which specifies a set of possible groups without revealing ...
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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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Size distribution of particles in Saturn’s rings from aggregation and fragmentation
Proceedings of the National Academy of Sciences of the United States of America, 2015Nikolai V Brilliantov +2 more
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