
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let R be a commutative ring with an identity 1R and let J be a proper ideal with the property that every element of R that is not in J is a unit of R . Prove that J is a maximal ideal of R .
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- Suppose that R is a commutative ring with unity and that I is an ideal of R. Prove that the set of all x ϵ R such that xn ϵ I for some positive integer n is an ideal of R.arrow_forwardLot R bx unity commutative ring with (1) Prove that if a ER, then a R={arIVER} а 1) an ideal of R (b) is aR a maximal ideal. aarrow_forward2) Let P + Q be maximal ideals in a ring R and a, b elements of R. Show that there exists c E R, such that a – cE P and b– cE Q.arrow_forward
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