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Factoring formal power series over principal ideal domains
power series principal ideal domains Commutative Algebra
2011/9/20
Abstract: We provide an irreducibility test and factoring algorithm (with some qualificiations) for formal power series in the unique factorization domain $R[[X]]$, where $R$ is any principal ideal do...
We address the problem of ambiguity of a function determined by an asymptotic perturbation
expansion. Using a modified form of the Watson lemma recently proved elsewhere, we discuss a
large class of...
Triangular Matrix Representations of Rings of Generalized Power Series
Generalized triangular matrix representation Twisted generalized power series ring PWP ring Triangulating dimension
2007/12/12
Let $R$ be a ring and $S$ a cancellative and torsion-free monoid and $\leq$ a strict order on $S$. If either $(S, \leq)$ satisfies the condition that $0\leq s$ for all $s\in S$, or $R$ is reduced, the...
Rickart-type Annihilator Conditions on Formal Power Series
Annihilator conditions Nearrings Skew power series Baer rings a-rigid rings Rickart rings
2010/2/25
Let R be an a-rigid ring and R0[[x;a]] be the nearring of a formal skew power series in which addition and substitution are used as operations. It is shown that R is Rickart and any countable family o...