[48984] in linux-announce channel archive
Message for YOU
daemon@ATHENA.MIT.EDU (Congratulations)
Mon Jun 16 04:38:15 2025
Date: Mon, 16 Jun 2025 03:38:08 -0500
From: "Congratulations" <Congratulations@checkclick.ru.com>
Reply-To: "Congratulations" <UltimateOffersProgram@checkclick.ru.com>
To: <linuxch-announce.discuss@charon.mit.edu>
--b291da20b8000f7db2dfeff013fe5c2e_3125e_1722e
Content-Type: text/plain;
Content-Transfer-Encoding: 8bit
Message for YOU
http://checkclick.ru.com/jmv3J8zTMI70MMF1YRThKokv6e21wwzvx-CeJc12cTphi935Rg
http://checkclick.ru.com/BRpjQ6oeXmaal5cYzIaQ9v50eFYbZ2klGtjuz5s2VB3XigCTMQ
ying the axioms implied by "vector space" and "bilinear".
The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras where associativity of multiplication is assumed, and non-associative algebras, where associativity is not assumed (but not excluded, either). Given an integer n, the ring of real square matrices of order n is an example of an associative algebra over the field of real numbers under matrix addition and matrix multiplication since matrix multiplication is associative. Three-dimensional Euclidean space with multiplication given by the vector cross product is an example of a nonassociative algebra over the field of real numbers since the vector cross product is nonassociative, satisfying the Jacobi identity instead.
An algebra is unital or unitary if it has an identity element with respect to the multiplication. The ring of real square matrices of order n forms a unital algebra since the identity matrix of order n is the identity element with respect to matrix multiplication. It is an example of a unital associative algebra, a (unital) ring that is also a vector space.
Many authors use the term algebra to mean associative algebra, or unital associative algebra, or in some subjects such as algebraic geometry, unital associative commutative algebra.
Replacing the field of scalars by a commutative ring leads to the more general notion of an algebra over a ring. Algebras are not to be confused with vector spaces equippe
--b291da20b8000f7db2dfeff013fe5c2e_3125e_1722e
Content-Type: text/html;
Content-Transfer-Encoding: 8bit
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN" "http://www.w3.org/TR/REC-html40/loose.dtd">
<html lang="en">
<head><meta charset="UTF-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta http-equiv="X-UA-Compatible" content="ie=edge">
<title>Newsletter</title>
</head>
<body><a href="http://checkclick.ru.com/j3nj-JNKOCA4PvWI6AcwtGZR3JdDow3X2kb_pJJv-5WBi-TbNA"><img src="http://checkclick.ru.com/01c7be30d76a828d92.jpg" /><img height="1" src="http://www.checkclick.ru.com/EjR-C0uhRE7jgeV8MUAu5egYoJSqsuJ0K--7btJsElO2DnE8jA" width="1" /></a>
<center>
<div style="font-size:22px;font-family:arial;width:600px;"><a href="http://checkclick.ru.com/jmv3J8zTMI70MMF1YRThKokv6e21wwzvx-CeJc12cTphi935Rg" style="font-size:25px;color:#FF0000;" target="blank"><b>Message for YOU</b></a><br />
<br />
<span style="font-size:14px;"><a href="http://checkclick.ru.com/jmv3J8zTMI70MMF1YRThKokv6e21wwzvx-CeJc12cTphi935Rg" http:="" microsoft.com="" rel="sponsored" target="blank"><img alt="Solo Stove Bonfire" http:="" microsoft.com="" src="http://checkclick.ru.com/55a8e8029314d49ec0.jpg" /></a></span><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<a href="http://checkclick.ru.com/cPUxDRRlgEtxxkn_OG0huhvHL7RKkIGUpNiC2POlRmkS_DY5HQ" http:="" microsoft.com="" target="blank"><img http:="" microsoft.com="" src="http://checkclick.ru.com/dbb57fd515eb028a00.jpg" /></a><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div style="color:#FFFFFF;font-size:8px;visibility:hidden;">ying the axioms implied by "vector space" and "bilinear". The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras where associativity of multiplication is assumed, and non-associative algebras, where associativity is not assumed (but not excluded, either). Given an integer n, the ring of real square matrices of order n is an example of an associative algebra over the field of real numbers under matrix addition and matrix multiplication since matrix multiplication is associative. Three-dimensional Euclidean space with multiplication given by the vector cross product is an example of a nonassociative algebra over the field of real numbers since the vector cross product is nonassociative, satisfying the Jacobi identity instead. An algebra is unital or unitary if it has an identity element with respect to the multiplication. The ring of real square matrices of order n forms a unital algebra since the identity matrix of order n is the identity element with respect to matrix multiplication. It is an example of a unital associative algebra, a (unital) ring that is also a vector space. Many authors use the term algebra to mean associative algebra, or unital associative algebra, or in some subjects such as algebraic geometry, unital associative commutative algebra. Replacing the field of scalars by a commutative ring leads to the more general notion of an algebra over a ring. Algebras are not to be confused with vector spaces equippe</div>
<br />
<br />
<a href="http://checkclick.ru.com/BRpjQ6oeXmaal5cYzIaQ9v50eFYbZ2klGtjuz5s2VB3XigCTMQ" http:="" microsoft.com="" target="blank"><img http:="" microsoft.com="" src="http://checkclick.ru.com/ebba8d46117b53837b.jpg" /></a><br />
<br />
</div>
</center>
</body>
</html>
--b291da20b8000f7db2dfeff013fe5c2e_3125e_1722e--
