In addition, Ds, Tfs) is the composite of D and D. Moreover, the ring Tcs) is the symmetric algebra S,(D,) of D, considered as a D-module. In the special case where S = D* = D\(O), we omit the superscript and let T denote the ring D XK, where s E S, we can conclude that many properties hold in because these properties are preserved by taking polynomial ring extensions and direct limits. If D is a commutative integral domain and S is a multiplicative system in D, then Tfs) = D XD, is the subring of the polynomial ring D, con- sisting of those polynomials with constant term in D.
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