A note on the elementary divisor theory in non-commutative domains

Abstract

Not only the number of the factors but the factors themselves are determined uniquely up to similarity.f We say that a two-sided ideal t is divisible by a if t^ (a)i D(a) r .This will be the case as soon as either t^ (a)j or t ü (a) r , as one can see easily.* In Ore-Jacobson's sense r-similarity corresponds to left-similarity.The element a is /"-similar to b if and only if there is an element c with (ca) r = (b) r 0 (c) r , (b) r U (c) r = /.t For this fact, although in our case it can be seen easily, see H.

Locations

• Project Euclid (Cornell University) - View - PDF
• Bulletin of the American Mathematical Society - View - PDF