Ascent and descent of going-down rings for integral extensions

Ascent and Descent for Sets of Operators

We extend the notion of ascent and descent for an operator acting on a vector space to sets of operators. If the ascent and descent of a set are both finite then they must be equal and give rise to a canonical decomposition of the space. Algebras of operators, unions of sets and closures of sets are treated. As an application we construct a Browder joint spectrum for commuting tuples of bounded...

Recursive Ascent-Descent Parsing

Generalized left-corner parsing was originally presented as a technique for generating a parser for the SLR(1) class of grammars but with far fewer states than the SLR(1) parser. This paper modi es and extends the formulation of left-corner parsers so that it is possible to apply the technique to the LALR(1) and LR(1) classes of grammars. It is further shown that left-corner parsers can be conv...

Extensions of Nilpotent P.P. Rings

Extensions of strongly alpha-reversible rings

We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...

Polynomial Ore Extensions of Baer and p.p.-Rings