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associated graded algebra; $QF$ algebra; $QF$-3 algebra; upper Loewy series; lower Loewy series

References:

[1] Auslander, M.: **Representation dimension of Artin algebras**. Queen Mary College Lecture Notes (1971). Zbl 0331.16026

[2] Morita, K.: **Duality for modules and its applications to the theory of rings with minimum condition**. Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A. No. 150 (1958), 1-60. MR 0096700 | Zbl 0080.25702

[3] Nakayama, T.: **On Frobeniusean algebras**. II, Ann. Math. 42 (1941), 1-21. DOI 10.2307/1968984 | MR 0004237 | Zbl 0026.05801

[4] Tachikawa, H.: **Quasi-Frobenius rings and generalizations**. LNM 351 (1973). Zbl 0271.16004

[5] Tachikawa, H.: **QF rings and QF associated graded rings**. Proc. 38th Symposium on Ring Theory and Representation Theory, Japan 45-51.\hfil http://fuji.cec.yamanash.ac.jp/ring/oldmeeting/2005/reprint2005/abst-3-2.pdf MR 2264126

[6] Thrall, R. M.: **Some generalizations of quasi-Frobenius algebras**. Trans. Amer. Math. Soc. 64 (1948), 173-183. MR 0026048 | Zbl 0041.01001