caa a22 4500 606160817 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10468-014-9512-9 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9512-9 Gorenstein Projective Modules Over a Class of Generalized Matrix Algebras and their Applications [Elektronische Daten] [Fang Li, Chang Ye] In this article, we introduce a class of generalized matrix algebras, in which each algebra is called a normally upper triangular gm algebra, and characterise Gorenstein projective modules over this class of algebras. Moreover, a sufficient condition of strongly Gorenstein projective modules over normally upper triangular gm algebras is given. The importance of normally upper triangular gm algebras for us is that it includes the so-called path algebras of quivers over algebras and generalized path algebras. Due to this, we characterize Gorenstein projective modules and strongly Gorenstein projective modules over path algebras of quivers over algebras and generalized path algebras as applications of the main results on normally upper triangular gm algebras. At last, we give an example to show how all indecomposable Gorenstein projective modules over a given algebra are constructed by the result on generalized path algebras. Springer Science+Business Media Dordrecht, 2014 Generalized matrix algebra nationallicence Generalized path algebra nationallicence Path algebra of quiver over an algebra nationallicence Gorenstein projective module nationallicence Strongly Gorenstein projective module nationallicence Li Fang Department of Mathematics, Zhejiang University (Yuquan Campus), 310027, Hangzhou, Zhejiang, People's Republic of China aut Ye Chang Department of Mathematics, Zhejiang University (Yuquan Campus), 310027, Hangzhou, Zhejiang, People's Republic of China aut Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 693-710 1386-923X 18:3<693 2015 18 10468 https://doi.org/10.1007/s10468-014-9512-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9512-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Fang Department of Mathematics, Zhejiang University (Yuquan Campus), 310027, Hangzhou, Zhejiang, People's Republic of China aut NATIONALLICENCE 700 1- Ye Chang Department of Mathematics, Zhejiang University (Yuquan Campus), 310027, Hangzhou, Zhejiang, People's Republic of China aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 693-710 1386-923X 18:3<693 2015 18 10468