From phma@webjockey.net Fri May 31 19:15:42 2002 Return-Path: X-Sender: phma@ixazon.dynip.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_3_2); 1 Jun 2002 02:15:41 -0000 Received: (qmail 56361 invoked from network); 1 Jun 2002 02:15:41 -0000 Received: from unknown (66.218.66.216) by m14.grp.scd.yahoo.com with QMQP; 1 Jun 2002 02:15:41 -0000 Received: from unknown (HELO neofelis.ixazon.lan) (208.150.110.21) by mta1.grp.scd.yahoo.com with SMTP; 1 Jun 2002 02:15:41 -0000 Received: by neofelis.ixazon.lan (Postfix, from userid 500) id 4672F3C499; Fri, 31 May 2002 22:15:35 -0400 (EDT) Content-Type: text/plain; charset="iso-8859-1" To: lojban@yahoogroups.com Subject: Algebra Date: Fri, 31 May 2002 22:15:33 -0400 X-Mailer: KMail [version 1.2] X-Spamtrap: fesmri@ixazon.dynip.com MIME-Version: 1.0 Message-Id: <02053122153303.02104@neofelis> Content-Transfer-Encoding: 8bit Sender: phma@ixazon.dynip.com From: Pierre Abbat X-Yahoo-Group-Post: member; u=92712300 There are at least four different meanings of "algebra, algebraic" in mathematics. I don't think it's right to call them all {aljebra}, so I try to come up with terms for them: 1. The basic meaning of "algebra" is manipulation of mekso. What's the word for "manipulate"? 2. Abstract algebra, in one sense, is the study of sujgri, piljygri, and dilcygri. So girzu saske. But what's the word for "operation"? (The other sense is algebra, in the first sense, in fields other than Q, R, or C. For instance, one can compute an elliptic curve sum by taking the formal derivative of a polynomial in a finite field and get sensible results, even though taking a derivative of a function in a finite field makes no sense.) 3. An algebra is a vector space with multiplication. {farlaili'i piljygri}? 4. An algebraic number is a number which is a solution to a polynomial equation. Any more suggestions? phma