User hector pinedo - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T10:06:02Z http://mathoverflow.net/feeds/user/26901 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109957/what-is-the-definition-of-the-picard-group-of-a-non-necessarilly-commutative-ri what is the definition of the Picard group of a (non necessarilly commutative) Ring? Hector Pinedo 2012-10-17T21:51:33Z 2012-10-18T06:31:00Z <p>Hi. I have only able to find the definition of $Pic(R)$ for a commutative ring $R.$ Which is the isomorphism classes of projective $R$-modules of rank $1,$ and the product given by $[A][B]=[A\otimes_R B].$</p> <p>How can i adapt this definition for the non-commutative case?</p> <p>are there some books of articles related to this ? Thanks.</p> http://mathoverflow.net/questions/108366/galois-extension-of-a-semi-local-ring/108461#108461 Answer by Hector Pinedo for Galois extension of a semi-local ring Hector Pinedo 2012-09-30T12:09:35Z 2012-09-30T12:09:35Z <p>Thanks a lot Doctor Andarkov. By the way, i just find an article where the autor proves that given a semi-local ring $R,$ every left $R$-module is semi-local.</p> <p>The article is On semilocal modules and rings Christian Lomp COMMUNICATIONS IN ALGEBRA, 27(4), 1921-1935 (1999)</p> <p>The result is in Theorem 3.5</p> http://mathoverflow.net/questions/109957/what-is-the-definition-of-the-picard-group-of-a-non-necessarilly-commutative-ri/109980#109980 Comment by Hector Pinedo Hector Pinedo 2012-12-01T00:22:31Z 2012-12-01T00:22:31Z Thanks a lot four your help. :)