Product of ring varieties and attainability
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- by Awad A. Iskander PDF
- Trans. Amer. Math. Soc. 193 (1974), 231-238 Request permission
Abstract:
The class of all rings that are Everett extensions of a ring in a variety $\mathfrak {U}$ by a ring in a variety $\mathfrak {B}$ is a variety $\mathfrak {U} \cdot \mathfrak {B}$. With respect to this operation the set of all ring varieties is a partially ordered groupoid (under inclusion), that is not associative. A variety is idempotent iff it is the variety of all rings, or generated by a finite number of finite fields. No families of polynomial identities other than those equivalent to $x = x$ or $x = y$ are attainable on the class of all rings or on the class of all commutative rings.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 193 (1974), 231-238
- MSC: Primary 16A48
- DOI: https://doi.org/10.1090/S0002-9947-1974-0349753-0
- MathSciNet review: 0349753