Noncommutative valuations
نویسندگان
چکیده
منابع مشابه
Noncommutative Valuations
The topic of this paper is the extension of the basic facts of valuation theory to noncommutative systems. The purpose of this generalization is twofold. First, the theory of valuations with commutative groups of values is placed in the framework of the theory of /-groups, and secondly the general theory leads to the construction of a new class of infinite division algebras. These division alge...
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This paper is a continuation of our recent joint work with K.H. Leung on the real spectrum of a noncommutative ring 15]. The object of the present paper is to develop a theory of real places and valuations to accompany the theory of orderings developed in 15]. Because of the existence of integral domains which are not embeddable in a skew eld, it is necessary to deal directly with integral doma...
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In a paper entitled Noncommutative valuations, Schilling [8] proved that if an algebra of finite order over its center is relatively complete in a valuation (where the value group of the nonarchimedean, exponential valuation is not assumed to be commutative) then the value group is commutative. A similar type of theorem, proved by Albert [l], states that if an algebra of finite order over a fie...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1945
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1945-08339-6