摘要 : Let F be an algebraically closed field of characteristic zero and G a finite cyclic group. Let V-G be a variety of associative G-graded PI-algebras over F of finite basic rank. In this paper, we prove that if V-G is minimal with r... 展开 Let F be an algebraically closed field of characteristic zero and G a finite cyclic group. Let V-G be a variety of associative G-graded PI-algebras over F of finite basic rank. In this paper, we prove that if V-G is minimal with respect to a given G-exponent, then there exist finite-dimensional G-simple F-algebras A(1),..., A(m) such that V-G is generated by a suitable G-graded upper block triangular matrix algebra UTG(A(1),..., A(m)) endowed with an elementary grading and where the diagonal blocks are given by the A(i)'s. Moreover, for a fixed m-tuple (A(1),..., A(m)) of finite-dimensional G-simple F-algebras, we prove the converse of the above result for some important classes of G-graded algebras A = UTG(A(1),..., A(m)) endowed with elementary gradings. In particular, we conclude that the variety generated by A is minimal when A has one or two G-simple blocks as well whenever all (except for at most one) the G-simple components of A are G-regular. 收起