Irreducible Divisor Graphs II

摘要

Let R be an integral domain, and let x  R be a nonzero nonunit that can be written as a product of irreducibles. Coykendall and Maney (to appear), defined the irreducible divisor graph of x, denoted G(x), as follows. The vertices of G(x) are the nonassociate irreducible divisors of x (each from a pre-chosen coset of the form π U(R) for π  R irreducible). Given distinct vertices y and z, we put an edge between y and z if and only if yz|x. Finally, if y n |x but y n+1  x, then we put n − 1 loops on the vertex y.In this article, inspired by the approach of the authors from Akhtar and Lee (to appear1. Akhtar , R. , Lee , L. Homology of zero divisors . To appear in Rocky Mountain J. Math. [Web of Science ®]View all references), we study G(x) using homology. A connection is found between H ₁ and the cycle space of G(x). We also characterize UFDs via these homology groups.View full textDownload full textRelated 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/10.1080/00927870802107967