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Research and Exposition in Mathematics -- Volume 17

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E.-A. Behrens

Arithmetical Completely Simple Semigroups

143 p., soft cover, ISBN 3-88538-217-2, EUR 25.00, 1989

To develop a non-commutative arithmetic for partially ordered semigroups the author defines arithmetical completely simple semigroups and applies them to the integral normal ideals in the central simple algebras Q over the quotient field of a Dedekind ring under a generalized multiplication. On the set I of the maximal orders in Q he introduces a partial order relation, the finer properties of which describe the arithmetic of Q.