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Dearomative ring expansion of thiophenes by bicyclobutane insertion
Science, 2023Skeletal ring enlargement is gaining renewed interest in synthetic chemistry and has recently focused on insertion of one or two atoms. Strategies for heterocyclic expansion through small-ring insertion remain elusive, although they would lead to the ...
Huamin Wang +7 more
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On schur rings of group rings of finite groups
Communications in Algebra, 1992Schur rings are rings associated to certain partitions of finite groups. They were introduced for applications in representation theory, cfr. [3][4]. The algebric structure of these rings has not been studied in depth. In this paper we determine explicit structure constants for Schur rings, we derive conditions for separability and we compute the ...
Apostolopoulou, C. +2 more
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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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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 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
openaire +1 more source