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Roth’s theorems and decomposition of modules. (English) Zbl 0468.16022

16GxxRepresentation theory of associative rings and algebras
15A24Matrix equations and identities
Full Text: DOI
[1] Bass, H.: Finitistic dimension and a homological generalization of semiprimary rings. Trans. amer. Math. soc. 95, 466-488 (1960) · Zbl 0094.02201
[2] Bourbaki, N.: Elements of mathematics, commutative algebra. (1972) · Zbl 0279.13001
[3] Gustafson, W.: Roth’s theorems over commutative rings. Linear algebra and appl. 23, 245-251 (1979) · Zbl 0398.15013
[4] Gustafson, W.; Zelmanowitz, J.: On matrix equivalence and matrix equation. Linear algebra and appl. 27, 219-224 (1979) · Zbl 0419.15009
[5] Hartwig, R.: Roth’s equivalence problem in unit regular rings. Proc. amer. Math. soc. 59, 39-44 (1976) · Zbl 0347.15005
[6] Jacobson, N.: The theory of rings. Amer. math. Soc. (1943) · Zbl 0060.07302
[7] Levy, L.; Robson, J.: Matrices and pairs of modules. J. algebra 29, 427-454 (1974) · Zbl 0282.16001
[8] Miyata, T.: Note on direct summands of modules. J. math. Kyoto univ. 7, 65-69 (1967) · Zbl 0189.03702
[9] Roth, W.: The equations AX-YB=C and AX-XB=C in matrices. Proc. amer. Math. soc. 3, 392-396 (1952) · Zbl 0047.01901
[10] Rotman, J.: Notes on homological algebra. (1970) · Zbl 0222.18003