On Herstein's theorems relating modularity in A and A(+)
ISSN: 0213-8743
Año de publicación: 1992
Volumen: 7
Número: 1
Páginas: 5-8
Tipo: Artículo
Otras publicaciones en: Extracta mathematicae
Resumen
In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal mentioned in paragraph 1 when the algebras involved are Jordan