so let x = k[a,b]/ab=1 ... then consider comm x-alg x[c]/c^2=a ... ???or something ...

???consider underlying module ... ???or something ???....

??something about basis 1,c ... ???so free module ??? .... or something ?? ...

hmmm....

??hmm, so what about morphisms between "self-inverse objects" in an ag theory?? ... vs between just ordinary invertible objects ... ???or something ... and so forth .... ????.....

??so what about whether there's a whole dimensional category (or something like that...) of self-inverse objects, in general ??? .... and so forth ...

??what about relationship of self-inverse objects to something about "real" and/or "bosonic", and so forth ??? ....

??what about something about ... ??possibility of ... ??interpreting "universal coefficients theorem" (or something... and so forth ...) in terms of ... ???something like ... ?property vs structure vs stuff (and so forth ...) analysis of things like "self-inverse object" ?? ... ???...

??so what about z/2-graded comm alg here ?? ... ...and so forth ... ???..

??hmm... ??what about strictness of commutativity here ?? ... ??? ... and so forth ... ???....

??so what _about_ laurent polynomials graded by Z/p according to residue of exponent ?? ...??what _is_ going on here ???? ....

??so what about removing multiplie points from affine line ?? ... ??...

??what about something about divisors and so forth here ?? ....