document.write( "Question 751133: What is an algebra
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Algebra.Com's Answer #457069 by Edwin McCravy(20055)\"\" \"About 
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document.write( "From wikipedia:\r\n" );
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document.write( "In mathematics, an algebra over a field is a vector space equipped with a\r\n" );
document.write( "bilinear product. An algebra such that the product is associative and has an\r\n" );
document.write( "identity is therefore a ring that is also a vector space, and thus equipped\r\n" );
document.write( "with a field of scalars. Such an algebra is called here a unital associative\r\n" );
document.write( "algebra for clarity, because there are also nonassociative algebras.\r\n" );
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document.write( "In other words, an algebra over a field is a set together with operations of\r\n" );
document.write( "multiplication, addition, and scalar multiplication by elements of the\r\n" );
document.write( "underlying field, that satisfy the axioms implied by \"vector space\"\r\n" );
document.write( "and \"bilinear\".[1]\r\n" );
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document.write( "One may generalize this notion by replacing the field of scalars by a\r\n" );
document.write( "commutative ring, and thus defining an algebra over a ring.\r\n" );
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document.write( "Because of the ubiquity of associative algebras, and because many textbooks\r\n" );
document.write( "teach more associative algebra than nonassociative algebra, it is common for\r\n" );
document.write( "authors to use the term algebra to mean associative algebra. However, this does\r\n" );
document.write( "not diminish the importance of nonassociative algebras, and there are texts\r\n" );
document.write( "that give both structures and names equal priority.\r\n" );
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document.write( "Wikipedia
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