An intertwining of a hereditary algebra and a cohereditary coalgebra


  • Hanni Garminia
  • Pudji Astuti
  • Irawati Irawati



Algebra, Coalgebra, Cohereditary, Hereditary,


Let 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.


Brzezinski T and Wisbauer R, Corings and comodules. London Mathematical Society Lecture Note Series, 309. Cambridge University Press, Cambridge, (2003)

Chin W. "Hereditary and Path Coalgebras", Comm. algebra 30,(2002) 1829-1831

Dascalescu S, Nastasescu C and Raianu S, Hopf Algebras. An Introduction. Monographs and Textbooks in Pure and Applied Mathematics, 235. Marcel Dekker, Inc., New York, (2001)

Jara L, Merino L, Llena D, and Stefan D, "Hereditary and Formally Smooth Coalgebras", Algebras and Representation Theory, 8(3) (2005) 363-374

Garminia H and Astuti P, "Karakterisasi Modul σ[M]-Koherediter", Majalah Ilmiah Himpunan Matematika Indonesia, (2006), 12(2), 225-231.

Garminia H, Astuti P, and Irawati "Properties of Cohereditary Comodules", Journal of Mathematics and Science, (2007), 12(2).

Natasescu C, Torrecillas B and Zhang Y H, "Hereditary coalgebras". Comm. Algebra 24 (1996) 1521-1528

Wisbauer R, Foundations of module and ring theory. A handbook for study and research. Gordon and Breach SciencePublishers, Philadelphia, PA, (1991)

Wisbauer R, "Tilting in module categories". Lecture Notes in Pure and Appl. Math., 201, Dekker, New York, (1998) 421–444.