Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n...Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n×n matrices over R for any positive integer n.We show that Sn(φ,R)■M_(n)(R)is a separable Frobenius extension.If R is commutative,then Sn(φ,R)is a cellular algebra over the invariant subring R^(φ)of R.展开更多
基金supported by Beijing Nova Program(Z181100006218010)by Research Ability Improvement Program of BUCEA(Grant No.X22026).
文摘Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n×n matrices over R for any positive integer n.We show that Sn(φ,R)■M_(n)(R)is a separable Frobenius extension.If R is commutative,then Sn(φ,R)is a cellular algebra over the invariant subring R^(φ)of R.
