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By P. M. Cohn (auth.), Rüstem Kaya, Peter Plaumann, Karl Strambach (eds.)

When trying to find purposes of ring concept in geometry, one first thinks of algebraic geometry, which occasionally will even be interpreted because the concrete facet of commutative algebra. despite the fact that, this hugely de­ veloped department of arithmetic has been handled in numerous mono­ graphs, in order that - regardless of its technical complexity - it may be considered as particularly good available. whereas within the final a hundred and twenty years algebraic geometry has time and again attracted centred interes- which instantaneously has reached a height once again - , the various different purposes of ring idea in geometry haven't been assembled in a textbook and are scattered in lots of papers in the course of the literature, which makes it demanding for them to emerge from the shadow of the intense thought of algebraic geometry. it's the objective of those complaints to offer a unifying presentation of these geometrical functions of ring theo~y outdoors of algebraic geometry, and to teach that they provide a substantial wealth of beauti­ ful rules, too. additionally it turns into obvious that there are ordinary connections to many branches of contemporary arithmetic, e. g. to the idea of (algebraic) teams and of Jordan algebras, and to combinatorics. To make those feedback extra distinctive, we are going to now supply an outline of the contents. within the first bankruptcy, an method in the direction of a thought of non-commutative algebraic geometry is tried from various issues of view.

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