Let-A-a-conmutative-ring-with-1-not-necessarily-a-whole-domain-Study-the-structure-that-has-A-x-with-the-usual-operations-Is-it-a-ring-always-Is-it-a-whole-domain-How-are-the-units-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 49235 by cesar.marval.larez@gmail.com last updated on 04/Dec/18

Let A a conmutative ring with 1 (not necessarily a whole domain). Study the structure that has A(x) with the usual operations Is it a ring always? Is it a whole domain? How are the units?

$${Let}\:{A}\:{a}\:{conmutative}\:{ring}\:{with}\:\mathrm{1}\: \\ $$$$\left({not}\:{necessarily}\:{a}\:{whole}\:{domain}\right). \\ $$$${Study}\:{the}\:{structure}\:{that}\:{has}\:{A}\left({x}\right)\: \\ $$$${with}\:{the}\:{usual}\:{operations} \\ $$$${Is}\:{it}\:{a}\:{ring}\:{always}? \\ $$$${Is}\:{it}\:{a}\:{whole}\:{domain}? \\ $$$${How}\:{are}\:{the}\:{units}? \\ $$

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Let-A-a-conmutative-ring-with-1-not-necessarily-a-whole-domain-Study-the-structure-that-has-A-x-with-the-usual-operations-Is-it-a-ring-always-Is-it-a-whole-domain-How-are-the-units-

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