A class of finite commutative rings constructed from Witt rings. (English) Zbl 1103.13016
Witt rings are well known in the algebraic theory of quadratic forms as are finitely generated reduced Witt rings of a formally real field. The authors begins with a well-studied class of rings, finitely generated reduced Witt rings and their generalizations, and uses a type of finite quotient ring to introduce a large class of finite commutative rings. These rings are not among the rings that arise naturally in the algebraic theory of quadratic forms.
The authors use the ideas and techniques of M. Knebusch, A. Rosenberg and R. Ware [Am. J. Math. 94, 119–155 (1972; Zbl 0248.13030)], to develop QWitt rings. A subclass of these rings, SQWitt rings, is quotients of Witt rings of fields. These rings are closely associated with quadratic forms theory. The authors provide some specific and clear examples in the paper under review; in particular they give an example that shows the difference between the maximal ideal behavior in QWitt and SQWitt rings.
The authors use the ideas and techniques of M. Knebusch, A. Rosenberg and R. Ware [Am. J. Math. 94, 119–155 (1972; Zbl 0248.13030)], to develop QWitt rings. A subclass of these rings, SQWitt rings, is quotients of Witt rings of fields. These rings are closely associated with quadratic forms theory. The authors provide some specific and clear examples in the paper under review; in particular they give an example that shows the difference between the maximal ideal behavior in QWitt and SQWitt rings.
Reviewer: Manouchehr Misaghian (Charlotte)
MSC:
| 13M05 | Structure of finite commutative rings |
| 11E81 | Algebraic theory of quadratic forms; Witt groups and rings |
| 12D15 | Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) |
Citations:
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