Given a commutative ring with identity R. A. Prove that a unit is not a zero...

Given a commutative ring with identity R.

A. Prove that a unit is not a zero divisor.

B. Prove that a zero divisor cannot be a unit.

Expert Solution

Colby Messinger answered 2 years ago

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Problem 2. Suppose that R is a commutative ring, and that R[X] := { (a_0, a_1,...

Problem 2. Suppose that R is a commutative ring, and that R[X] := { (a_0, a_1, a_2, ...)^T | a_i is in R, a_i not equal to 0 for only finitely many i} is the set of polynomials over R, where we have named one particular element X := (0, 1, 0, 0, . . .)T . Show that R[X] forms a commutative ring with a suitably-chosen addition and multiplication on R[X]. This will involve specifying a “zero” element of...

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Given a commutative ring with identity R. A. Prove that a unit is not a zero...

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