1982/03/01 by Desmond Fearnley‐Sander · 1 citation
Mathematics · Social Sciences · Psychology · #History and Theory of Mathematics #Mathematics and Applications #Mathematics Education and Teaching Techniques #Sketch #Subject (documents) #Algebra over a field #Universal algebra #Set (abstract data type) #Mathematics #Hindsight bias #Pure mathematics #Computer science #Psychology #Algorithm #Library science
paper · doi:10.1080/00029890.1982.11995404
openalex publication_date 1982/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Algebras variety Moderne Algebra Hohere Algebra becomes a linear space if we define addition and multiplication by scalars in the natural way, and indeed it becomes a (nonassociative) linear algebra over if we define (6 ) (6 ) = 6 ( ) where we need an obvious convention to cope with the fact that the indices and may range over different finite sets of natural numbers. This is the on over . The free algebra may be put to work in the following way. A linear algebra is said to satisfy the (or ) 6 = 0 where 6 , if a valid equation is obtained whenever all the free algebra generators on the left are replaced by elements of The algebras satisfying a fixed set of laws form what is called a of algebras. A typical law of degree 3, for example, is ( ) = ( ) ; it determines the variety of associative algebras. (Here, as is usual, we have omitted the outermost brackets.) There are some branches of mathematics to which one may arguably assign a clearly defined starting point. In the c...