Non-commutative rings of fractions in algebraical approach to control theory. (English) Zbl 0874.16023

The algebraic construction of the ring of fractions, generalized for non-commutative rings, is described in the paper. The results of O. Ore from 1931 are elaborated to be applicable in the systems and control theory: including zero divisors, allowing a special set of denominators, showing a duality between left and right fractions, studying morphisms and including further operations on rings. Finally, a concrete application in the systems and control theory is shown.
Reviewer: J.Duda (Brno)


16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
93B25 Algebraic methods
16U20 Ore rings, multiplicative sets, Ore localization
93A99 General systems theory
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