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Showing 1 to 4 of 4 for “"Ring Extension"”.
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Differential Polynomial Rings: Order Properties and Morita Equivalence
… thesis is concerned with the behavior of certain ring properties with respect to the ring extension R (--->) R{X,(delta)}, where the latter is the ring of differential polynomials. Three properties are considered.
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Transcendence degree in power series rings
Let D[[X]] be the ring of formal power series over the commutative integral domain D. Gilmer has shown that if K is the quotient field of D, then D[[X]] and K[[X]] have the same quotient field if and only if K[[X]] ~ D[[X]]D_(O). Further, if a is any nonzero element of D, Sheldon has shown that …
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Weak Purity for Gorenstein Rings
… branch locus theorem states that a module finite ring extension of local normal domains $B\to A$ which is unramified in codimension one, with B a regular local ring, is unramified (and in this setting, etale). When the ring B is merely Gorenstein, there are numerous examples which show that A need …