product ring
product ring noun: a ring that is the direct product of rings.
Noun
product ring (plural product rings)
- A ring that is the direct product of rings.
- For instance, let X be an infinite set, R the product ring K^(XY)#92;#33;, and A the set of homomorphisms R#92;rightarrowK given by evaluation at all the elements of X. Then the hypothesis of the Lemma holds, but #92;text#123;Int#125;#95;A(R) is the product ring k^(XY)#92;#33;, which is not in...1996, George M. Bergman, Adam O. Hausknecht, Cogroups and Co-rings in Categories of Associative Rings, American Mathematical Society, page 246
- Thus the set X#92;timesY 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#92;#33;, respectively.2003, Erdoğan S. Şuhubi, Functional Analysis, Springer, page 63
- Synonyms:
- direct product ring
Synonyms of product ring
- direct product ring
Forms of product ring
| plural | product rings |
|---|
Words formed from product ring
- cup product ring
- semidirect product ring
Questions about product ring
- What does product ring mean?
- Product ring means a ring that is the direct product of rings.
- What part of speech is product ring?
- Product ring is a noun.
- What is the plural of product ring?
- The plural of product ring is product rings.
Words near product ring in the dictionary
Source and license
Adapted from Wiktionary: product ring (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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