Basic Algebras

A basic algebra is a finite dimensional algebra A over a field, all of whose simple modules have dimension one. In the literature such an algebra is known as a ``split'' basic algebra. The type in Magma is optimized for the purposes of doing homological calculations.

• Creation from a sequence of projective modules and a path tree for each module
• Creation of the basic algebra corresponding to the group algebra of a p-group over GF(p).
• Arithmetic
• Extension and restriction of the coefficient ring
• Tensor product
• Opposite algebra
• Construction of modules over basic algebras
• Submodules, quotient modules, radicals and socles
• Projective covers and injective hulls
• Algebra as a right regular module over itself