product ring
Noun
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Noun
product ring (plural product rings)
- (mathematics, ring theory) A ring that is the direct product of rings.
- 1996, George M. Bergman, Adam O. Hausknecht, Cogroups and Co-rings in Categories of Associative Rings, American Mathematical Society, page 246 ↗,
- For instance, let X be an infinite set, R the product ring K^XY\!, and A the set of homomorphisms R \rightarrow K given by evaluation at all the elements of X. Then the hypothesis of the Lemma holds, but \text{Int}_A(R) is the product ring k^XY\!, which is not in general free as a k-module.
- 2003, Erdoğan S. Şuhubi, Functional Analysis, Springer, page 63 ↗,
- Thus the set X \times Y becomes a ring with these operations and it is called the product ring. The identity element of the product ring with respect to the addition is obviously (0,0) where 0 and 0 are identity elements of addition in the rings X and Y\!, respectively.
- 2007, Catriona Maclean (translator), Daniel Perrin, Algebraic Geometry: An Introduction, [1995, D. Perrin, Géométrie algébrique], Springer, page 101 ↗,
- Then A_\lambda is isomorphic to the product ring k \times k via the homomorphism sending X to (\alpha,-\alpha).
- 1996, George M. Bergman, Adam O. Hausknecht, Cogroups and Co-rings in Categories of Associative Rings, American Mathematical Society, page 246 ↗,
- (ring that is the direct product of rings) direct product ring
- French: produit d'anneaux
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