Research and Exposition in Mathematics -- Volume 17
Enlarged Picture
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.