An intertwining of a hereditary algebra and a cohereditary coalgebra
Keywords:Algebra, Coalgebra, Cohereditary, Hereditary,
AbstractLet F be a field. It is known that if A is a finitely dimensional hereditary F -algebra then the dual A∗ =HomF(A,F) is a
cohereditary F -coalgebra. On the other hand if C is a finitely dimensional cohereditary F -coalgebra then the
dual ( ) F C∗ =Hom C,F is a hereditary F -algebra. As a result, if C is a finitely dimensional F -coalgebra then C is
a cohereditary F -coalgebra if and only if the dual C∗ is a hereditary F -algebra. In this paper we enlarge the class of
algebras and coalgebras under consideration. Particularly we show that properties similar to the above results are
obtained for a class of algebras and coalgebras over a self injective commutative ring R where the algebras and
coalgebras, as R -modules, are locally projective.
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