Introduction

Yurij A. Drozd and Vladimir V. Kirichenko
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Yurij A. Drozd: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics
Vladimir V. Kirichenko: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics

Chapter 1 in Finite Dimensional Algebras, 1994, pp 1-30 from Springer

Abstract: Abstract An algebra over a field K, or a K-algebra, is a vector space A over the field K together with a bilinear associative multiplication. In other words, to any two elements a and b from the space A, taken in a definite order, there corresponds a uniquely defined element from A which is usually called their product and denoted by ab, whereby the following axioms are satisfied: 1) a(b + c) = ab + ac; 2) (b + c)a = ba + ca; 3) (αa)b = a(αb) = a(αb); 4) (ab)c = a(bc), where a, b, c are arbitrary elements from A and α an arbitrary element (scalar) of the field K.

Keywords: Factor Module; Division Algebra; Jordan Algebra; Congruence Class; Quotient Algebra (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-3-642-76244-4_1

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