Du, Jie; Lin, Zongzhu Stratifying algebras with near-matrix algebras. (English) Zbl 1044.16006 J. Pure Appl. Algebra 188, No. 1-3, 59-72 (2004). For a left module \(U\) and a right module \(V\) over an algebra \(D\) with a \(D\)-\(D\) bilinear form \(\beta\colon U\times V\to D\), an associative algebra structure can be defined on the tensor product \(V\otimes_DU\) which is called a near matrix algebra. In the present paper, the authors investigate algebras filtered by near matrix algebras and establish a unified treatment of quasi-hereditary algebras, cellular algebras and stratified algebras. Reviewer: Zhang Hechun (Beijing) Cited in 2 Documents MSC: 16G20 Representations of quivers and partially ordered sets 16P10 Finite rings and finite-dimensional associative algebras 20G05 Representation theory for linear algebraic groups 16S50 Endomorphism rings; matrix rings 16W70 Filtered associative rings; filtrational and graded techniques Keywords:near matrix algebras; hereditary algebras; stratified algebras PDFBibTeX XMLCite \textit{J. Du} and \textit{Z. Lin}, J. Pure Appl. Algebra 188, No. 1--3, 59--72 (2004; Zbl 1044.16006) Full Text: DOI References: [1] Auslander, M.; Reiten, I.; Smalo, S. O., Representation Theory of Artin Algebras (1997), Cambridge University Press: Cambridge University Press Cambridge [2] Cline, E.; Parshall, B.; Scott, L., Finite dimensional algebras and highest weight categories, J. Reine Angew. Math., 391, 85-99 (1988) · Zbl 0657.18005 [3] Cline, E.; Parshall, B.; Scott, L., Integral and graded quasi-hereditary algebras, J. Algebra, 131, 126-160 (1990) · Zbl 0699.16015 [4] Cline, E.; Parshall, B.; Scott, L., Stratifying endomorphism algebras, Mem. AMS, 591 (1996) · Zbl 0888.16006 [6] Du, J.; Parshall, B.; Scott, L., Stratifying endomorphism algebras associated to Hecke algebras, J. Algebra, 203, 169-210 (1998) · Zbl 0920.20008 [7] Du, J.; Rui, R., Based algebras and standard bases for quasi-hereditary algebras, Trans. Amer. Math. Soc., 350, 3207-3235 (1998) · Zbl 0908.16015 [8] Graham, J.; Lehrer, G., Cellular algebras, Invent. Math., 123, 1-34 (1996) · Zbl 0853.20029 [9] Wiedemann, A., On stratifications of derived module categories, Canad. Math. Bull., 34, 275-280 (1991) · Zbl 0753.16006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.