Local-Global Criteria for Outer Product Rings
| Autor: | Jacob R. Matijevic, Dennis R. Estes |
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| Rok vydání: | 1980 |
| Předmět: | |
| Zdroj: | Canadian Journal of Mathematics. 32:1353-1360 |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/cjm-1980-105-1 |
| Popis: | Let R be a commutative ring with multiplicative identity. We say that R is an outer product ring (OP-ring) if each vector v in the exterior power ⋀nRn+1 is decomposable; i.e. v = v1 ⋀ v2 ⋀ … ⋀ vn with vi ∈ Rn+1 (alternatively, each n + 1 tuple of elements in R is the tuple of n × n minors of some n × (n + 1) matrix with entries in R).Lissner initiated the study of which commutative rings are OP-rings, showing that any Dedekind domain is an OP-ring [13]. Towber classified the local Noetherian OP-rings as those with maximal ideal generated by two elements, and Hinohara's reformulation of Towber's result extended the context to semi-local rings [18, 11]. Assuming the stronger condition that all Pliicker vectors are decomposable and designating such rings as Towber rings, Lissner and Geramita gave necessary conditions for a Noetherian ring to be a Towber ring [14]. |
| Databáze: | OpenAIRE |
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