Journal of the Ramanujan Mathematical Society

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When is (K, K[y1,....,yt) an N-ring Pair?


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1 Department of Mathematics, Saurashtra University, Rajkot 360005, India
     

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For a commutative ring T with identity and a subring RofT containing the identity element of T, (R, T) is called an N-ring pair if each subring A of T such that R ⊆ A is an N-ring. In Section 2 we characterize when (K, T) is an AT-ring pair where T = K[Y1,..., Yt] is an affine ring over a field K. In Section 3 we determine when (R, T) is an iV-ring pair where T = R[x%,..., xn] is the polynomial ring in n variables x1,... ,xn over a ring R.
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  • When is (K, K[y1,....,yt) an N-ring Pair?

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Authors

S. Visweswaran
Department of Mathematics, Saurashtra University, Rajkot 360005, India

Abstract


For a commutative ring T with identity and a subring RofT containing the identity element of T, (R, T) is called an N-ring pair if each subring A of T such that R ⊆ A is an N-ring. In Section 2 we characterize when (K, T) is an AT-ring pair where T = K[Y1,..., Yt] is an affine ring over a field K. In Section 3 we determine when (R, T) is an iV-ring pair where T = R[x%,..., xn] is the polynomial ring in n variables x1,... ,xn over a ring R.