Abstract algebra (ring theory)

Thread starter ewup
Start date Dec 6, 2008
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Abstract Abstract algebra Algebra Theory

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The set R, consisting of rational numbers whose reduced form has a denominator not divisible by a fixed prime p, is verified to be a ring under standard addition and multiplication. The discussion explores the properties of R, confirming it satisfies ring axioms such as closure, associativity, and the existence of additive identity and inverses. Invertible elements in R are identified as those rational numbers whose numerators are not divisible by the prime p. The conversation concludes with an invitation for further engagement on the topic. This exploration of ring theory highlights the structure and characteristics of R in abstract algebra.

Dec 6, 2008

ewup

Let R be the set of all a in rational numbers in whose reduced form the denominator is not divisible by a fixed prime p. Verify R is a ring under the usual addition and multiplication in rational numbers. Find all invertible elements in R.

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Dec 6, 2008

Hurkyl

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Done! How about you?

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