The Category of Firm Modules for Nonunital Monomial Algebras

摘要

Let k be a field and X a set and P be a set of words over X. Consider the free nonunital k-algebra over X generated by the nonempty words over X and let R be the quotient of this algebra modulo the ideal generated by the words in P. R is called a “nonunital monomial algebra”. A right R-module M is said to be “firm” if M _R R → M given by m r mr is an isomorphism. In this article we prove that if R is a nonunital monomial algebra, the category of firm modules is Grothendieck.View full textDownload full textKey WordsAbelian categories, Firm modules, Monomial algebras, Nonunital rings2000 Mathematics Subject Classification16D90, 18E10Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870701776888