Noncommutative Valuations
نویسنده
چکیده
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 algebras are of highly transcendental structure over their respective centers ; moreover they may be considered, in special cases, as crossed transcendental extensions of other division algebras. I t is necessary to recall some facts on /-groups. A group T is called a simply ordered /-group if the following axioms are satisfied : (I) There is defined a binary inclusion relation which is "homogeneous" in the sense that ce^jS implies p+a+a^fi+P+cr for all p, cr, (II) r is a lattice with respect to the ordering relation, and (III) given 0 all £€Er satisfying £ < ô.
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