### On ideal and subalgebra coefficients in a class *k*-algebras

#### Abstract

Let

*k*be a commutative field with prime field and A a*k*- algebra. Moreover, assume that there is a*k*-vector space basis of A that satisfies the following condition: for all ,the product is contained in the -vector space spanned by . It is proven that the concept of minimal field of definition from polynomial rings and semigroup algebras can be generalized to the above class of (not necessarily associative)*k*-algebras. Namely, let U be a one-sided ideal in A or a*k*-subalgebra of A. Then there exists a smallest with U-as one-sided ideal resp. as*k*-algebra—being generated by elements in the -vector space spanned by .DOI Code:
10.1285/i15900932v27n1p77

Keywords:
Field of definition; Non-associative

*k*-algebra; One-sided ideal;*k*-subalgebraFull Text: PDF PS