Title 



Hereditary coalgebras
 
Author 



 
Abstract 



In this note, we study the global dimension of coalgebras and discuss the class of coalgebras of global dimension less or equal to 1. The coalgebras in this class, which contains all the cosemisimple coalgebras, are called hereditary coalgebras. If C is a finite dimensional coalgebra, then C is hereditary if and only if C* (the convolution algebra of C) is a hereditary algebra. Any direct sum of hereditary coalgebras is hereditary too. This gives us many examples of infinite dimensional hereditary coalgebras. A coalgebra is left hereditary if and only if it is right hereditary. Moreover, there do not exist hereditary Hopf algebras of finite dimension which are not cosemisimple.   
Language 



English
 
Source (journal) 



Communications in algebra.  New York, N.Y.  
Publication 



New York, N.Y. : 1996
 
ISSN 



00927872
 
Volume/pages 



24:4, p. 15211528
 
ISI 



A1996UC85200019
 
Full text (Publisher's DOI) 


  
