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Canadian Mathematical Bulletin, 1971
In this brief exposition we collect several results on rings of formal power series with coefficients from a field or a ring with some special properties. The results that are catalogued below are mostly algebraic in nature.
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In this brief exposition we collect several results on rings of formal power series with coefficients from a field or a ring with some special properties. The results that are catalogued below are mostly algebraic in nature.
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Polynomial and Power Series Rings
1960Among commutative rings, the polynomial rings in a finite number of indeterminates enjoy important special properties and are frequently used in applications. As they are also of paramount importance in Algebraic Geometry, polynomial rings have been intensively studied.
Oscar Zariski, Pierre Samuel
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Isonoetherian power series rings
Communications in Algebra, 2017ABSTRACTFacchini and Nazemian proved that a valuation domain is isonoetherian if and only if it is discrete of Krull dimension ≤2 and they showed that this cannot be generalized from the local case to the global case: the 2-dimensional generalized Dedekind domain ℤ+Xℚ[[X]] is not isonoetherian. Let D be an integral domain with quotient field K.
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Generalized Power Series Rings
1990Let R be a commutative ring, with unit element 1. Let S be a commutative monoid written multiplicatively (except when written additively...); thus, S is a semigroup with unit element, also denoted 1. We assume that S is endowed with a compatible strict order relation ≤, which is not necessarily a total order.
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Idempotents of 2 × 2 matrix rings over rings of formal power series
Linear and Multilinear Algebra, 2022Vesselin Drensky
exaly
Dimension Theory in Iterated Local Skew Power Series Rings
Algebras and Representation Theory, 2022William Woods
exaly