Adjoining a universal inner inverse to a ring element

作者：Bergman George M^*

来源：Journal of Algebra, 2016, 449: 355-399.

DOI：10.1016/j.jalgebra.2015.11.008

• Universal adjunction of an inner
• inverse to an element of a k-algebra
• Normal forms in rings and modules

Let R be an associative unital algebra over a field k, let p be an element of R, and let R' = R < q vertical bar pqp = p). We obtain normal forms for elements of R', and for elements of R'-modules arising by extension of scalars from R-modules. The details depend on where in the chain pR boolean AND Rp subset of pR boolean OR Rp subset of pR + Rp subset of R the unit 1 of R first appears.
This investigation is motivated by a hoped-for application to the study of the possible forms of the monoid of isomorphism classes of finitely generated projective modules over a von Neumann regular ring; but that goal remains distant. We end with a normal form result for the algebra obtained by tying together a k-algebra R given with a nonzero element p satisfying 1 is not an element of pR Rp and a k-algebra S given with a nonzero q satisfying 1 is not an element of qS + Sq, via the pair of relations p = pqp, q = qpq.

• 出版日期2016-3-1