We interoduce a new characterization of algebras of normal forms of term rewriting systems [35] as algerbras of term free in itself (any function from free generators into the algebra generates endomorphism of the algebra). Introduced algebras are free in classes of algebras satisfying some sets of equalities. Their universes are subsets of all terms and the denotations of operation symbols are...

Hecke endomorphism algebras are endomorphism algebras over a Hecke algebra associated to a finite Weyl group W of certain q-permutation modules, the “tensor spaces.” Such a space may be defined for any W in terms of a direct sum of certain cyclic modules associated to parabolic subgroups. The associated algebras have important applications to the representations of finite groups of Lie type. In...

Let S be the left R-bialgebroid of a depth two extension with cen-tralizer R. We show that the left endomorphism ring of depth two extension, not necessarily balanced, is a left S-Galois extension of A op. Looking to examples of depth two, we establish that a Hopf subalgebra is normal if and only if it is a Hopf-Galois extension. We find a class of examples of the alternative Hopf algebroids in...

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a “normal” circulant, so the automorphism group is contained in the normalizer of a cycle. Then we use these characterizations to prove results on the automorph...

For any complete chain I whose distinct elements are separated by cover pairs, and for every family {Mi | i∈ I} of monoids, we construct a family of graphs {Gi | i∈ I} such that Gi is a proper induced subgraph of Gj for all i; j∈ I with i ¡ j, Gi = ⋂ {Gj | j∈ I; i ¡ j} whenever i = inf{ j∈ I | j¿ i} in I , Gi = ⋃ {Gj | j∈ I; j ¡ i} whenever i = sup{ j∈ I | j¡ i} in I , the endomorphism monoid o...

It is well-known that modules with pathological properties can be obtained by constructing modules with \nearly prescribed" endomorphism rings. (See, for example, [5], [2], [3], or [10].) Here we shall investigate that method using a rather weak notion of nearly prescribing the endomorphism ring, namely one that just requires that a certain ring be algebraically closed in the endomorphism ring ...