Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414448 | Journal of Algebra | 2015 | 33 Pages |
It is proved that the prime degenerate (â1,1) algebra constructed in [12] (the (â1,1)-monster) generates the same variety of algebras as the Grassmann (â1,1)-algebra. Moreover, the same variety is generated by the Grassmann envelope of any simple nonassociative (â1,1)-superalgebra. The variety occurs to be the smallest variety of (â1,1)-algebras that contains prime nonassociative algebras.Similar results are obtained for Jordan algebras. Thus, the Jordan monster (the prime degenerate algebra constructed in [12]) and the Grassmann envelope of the prime Jordan superalgebra of vector type have the same ideals of identities. It is also shown that the Jordan monster generates a minimal variety that contains prime degenerate Jordan algebras.All the algebras and superalgebras are considered over a field of characteristic 0.