On the unique factorization theorem for formal power series
نویسندگان
چکیده
منابع مشابه
Unique Factorization Theorem and Formal Concept Analysis
In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present a new, less complicated, proof of this theorem that is based on Formal Concept Analysis. The method of the proof can be successfully applied...
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Let G be a finite group, k a perfect field, and V a finite dimensional kG-module. We let G act on the power series k[[V ]] by linear substitutions and address the question of when the invariant power series k[[V ]] form a unique factorization domain. We prove that for a permutation module for a p-group in characteristic p, the answer is always positive. On the other hand, if G is a cyclic group...
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Let K be a field of characteristic zero and let K((R≤0)) denote the ring of generalized power series (i.e., formal sums with well-ordered support) with coefficients in K, and non-positive real exponents. Berarducci (2000) constructed an irreducible omnific integer, in the sense of Conway (2001), by first proving that an element of K((R≤0)) that is not divisible by a monomial and whose support h...
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A property of graphs is any class of graphs closed under isomorphism. A property of graphs is induced-hereditary and additive if it is closed under taking induced subgraphs and disjoint unions of graphs, respectively. Let P1,P2, . . . ,Pn be properties of graphs. A graph G is (P1,P2, . . . ,Pn)-partitionable (G has property P1◦P2◦ · · · ◦Pn) if the vertex set V (G) of G can be partitioned into ...
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The concept of an object-system is a common generalization of simple graph, digraph and hypergraph. In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present UFT for object-systems. This result gene...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1967
ISSN: 2156-2261
DOI: 10.1215/kjm/1250524274