Semisimple artinian graded rings

Artinian rings, finite principal ideal rings and algebraic error-correcting codes

“…For a polynomial ring Q = R[xi,... ,x n ], and an ideal I C Q generated by univariate polynomials, conditions are obtained for Q/I to be a principal ideal ring when R is a principal ideal ring and Q/I is finite. Conditions are also provided 526 J. Cazaran [2] for Q/I to be a direct sum of finite fields or Galois rings. Part of Chapter 3 appears in [3].…”

“…All semigroup varieties, V, are described such that the semigroup algebra FS is semisimple Artinian, for every finite semigroup S S V, where F is an arbitrary field. Most of Chapter 5 appears in [2].…”