Volume 36 • Number 2 • 2013   • $(a,b,c)$-Koszul Algebras Jia-Feng Lü Abstract. Given fixed integers $a,\;b$ and $c$ with $a>c>b>1$, the notion of {\it $(a,b,c)$-Koszul algebra} is introduced, which is another extension of Koszul algebras and includes some Artin-Schelter regular algebras of global dimension five as special examples. Some criteria for a standard graded algebra to be $(a,b,c)$-Koszul are given. Further, the Yoneda algebras and the $H$-Galois graded extensions of $(a,b,c)$-Koszul algebras are discussed, where $H$ is a finite dimensional semisimple and cosemisimple Hopf algebra. Moreover, the so-called {\it (generalized) $(a,b,c)$-Koszul modules} are introduced and some basic properties are also provided. 2010 Mathematics Subject Classification: Primary 16S37, 16W50; Secondary 16E30, 16E40 Full text: PDF