From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1566 Path: news.gmane.org!not-for-mail From: "Osher Doctorow" Newsgroups: gmane.science.mathematics.categories Subject: category theory analysis of the Jacobson radical Date: Tue, 11 Jul 2000 16:20:52 -0700 Message-ID: <000001bfeb8e$fa331b80$74f46ed1@osherphd> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000F_01BFEB53.FB901540" X-Trace: ger.gmane.org 1241017928 31843 80.91.229.2 (29 Apr 2009 15:12:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:12:08 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Wed Jul 12 10:29:35 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA09488 for categories-list; Wed, 12 Jul 2000 10:26:48 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 8 Original-Lines: 90 Xref: news.gmane.org gmane.science.mathematics.categories:1566 Archived-At: This is a multi-part message in MIME format. ------=_NextPart_000_000F_01BFEB53.FB901540 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable From: Osher Doctorow osher@ix.netcom.com, Tues. July 11, 2000, 4:15PM Dear Colleagues: The Jacobson radical that I have been mentioning in the last several = communications, and which is defined in terms of the circle composition = product x * y =3D x + y - xy, is related to category theory by M. W. = Gray (Pacific Jour. Math 1967, vol. 23, 79-89 and her book A radical = approach to algebra, Addison-Wesley: Reading, 1970. In particular, the = semiabelian category was introduced by her to include various of the = radicals including the Jacobson radical. A very accessible detailed = presentation of her work and those of others up to 1994 is T. W. Palmer = Banach algebras and the general theory of *-algebras volume I: algebras = and Banach algebras, Cambridge University Press: Cambridge, which is = part of the exceptionally valuable Encyclopedia of Mathematics and Its = Applications of the Cambridge University Press (not of course a usual = encyclopedia - the name is used for numerous separate books of the = highest quality on crucial mathematical subjects important in the latest = rsearch). See especially sections 4.3 and 4.7. I will give more details on this at a future time. Osher Doctorow ------=_NextPart_000_000F_01BFEB53.FB901540 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
From: Osher Doctorow osher@ix.netcom.com, Tues. July = 11, 2000,=20 4:15PM
 
Dear Colleagues:
 
The Jacobson radical that I have been = mentioning in=20 the last several communications, and which is defined in terms of the = circle=20 composition product x * y =3D x + y - xy, is related to category theory = by M. W.=20 Gray (Pacific Jour. Math 1967, vol. 23, 79-89 and her book A radical = approach to=20 algebra, Addison-Wesley: Reading, 1970.  In particular, the = semiabelian=20 category was introduced by her to include various of the radicals = including the=20 Jacobson radical.  A very accessible detailed presentation of her = work and=20 those of others up to 1994 is T. W. Palmer Banach algebras and the = general=20 theory of *-algebras volume I: algebras and Banach algebras, Cambridge=20 University Press: Cambridge, which is part of the exceptionally valuable = Encyclopedia of Mathematics and Its Applications of the Cambridge = University=20 Press (not of course a usual encyclopedia - the name is used for = numerous=20 separate books of the highest quality on crucial mathematical subjects = important=20 in the latest rsearch).   See especially sections 4.3 and=20 4.7.
 
I will give more details on this at a = future=20 time.
 
Osher Doctorow
 
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