Local-Global Criteria for Outer Product Rings

Estes, Dennis R. ; Matijevic, Jacob R.

Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1353-1360

Résumé

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 ⋀n Rn+1 is decomposable; i.e. v = v1 ⋀ v2 ⋀ ... ⋀ v n with v i ∈ 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].

Détail

DOI : 10.4153/CJM-1980-105-1

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