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Roth’s theorems over commutative rings. (English) Zbl 0398.15013

MSC:
15A24Matrix equations and identities
15A06Linear equations (linear algebra)
15B33Matrices over special rings (quaternions, finite fields, etc.)
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Full Text: DOI
References:
[1] Bourbaki, N.: Élements de mathématique: algèbre commutative. Actualités scientific et industrielles no. 1293 (1961)
[2] Bourbaki, N.: Élements de mathématique: algèbre commutative. Actualités scientifiques et industrielles no. 1290 (1961)
[3] Feinberg, R. B.: Similarity of partitioned matrices. J. res. Nat. bur. Standards, sect. B 79B, 117-125 (1975) · Zbl 0332.15005
[4] Feinberg, R. B.: Equivalence of partitioned matrices. J. res. Nat. bur. Standards, sect. B 80B, 89-97 (1976) · Zbl 0337.15015
[5] W.H. Gustafson, On the matrix equations AX-YB = C and AX-XB = C, J. Res. Nat. Bur. Standards, Sect. B, to appear.
[6] Hartwig, R. E.: Roth’s equivalence problem in unit regular rings. Proc. amer. Math. soc. 59, 39-44 (1976) · Zbl 0347.15005
[7] Roth, W. E.: The equations AX-YB = C and AX-XB = C in matrices. Proc. amer. Math. soc. 3, 392-396 (1952) · Zbl 0047.01901