Weak Normality and Strong t-closedness of Generalized Power Series Rings
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초록
For an extension A ⊆ B of commutative rings, we present a sufficient condition for the ring [[A^{S}, ^{≤}]] of generalized power series to be weakly normal (resp., strongly t-closed) in [[B^{S}, {≤}]], where (S, ≤) be a torsion-free cancellative strictly ordered monoid. As a corollary, it can be applied to the ring of power series in infinitely many indeterminates as well as in finite indeterminates.
Abstract
For an extension A ⊆ B of commutative rings, we present a sufficient condition for the ring [[A^{S}, ^{≤}]] of generalized power series to be weakly normal (resp., strongly t-closed) in [[B^{S}, {≤}]], where (S, ≤) be a torsion-free cancellative strictly ordered monoid. As a corollary, it can be applied to the ring of power series in infinitely many indeterminates as well as in finite indeterminates.
참고문헌 (6)
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