Direct decompositions
HTML articles powered by AMS MathViewer
- by Reinhold Baer PDF
- Trans. Amer. Math. Soc. 62 (1947), 62-98 Request permission
References
- A. A. Albert, Quasigroups. I, Trans. Amer. Math. Soc. 54 (1943), 507–519. MR 9962, DOI 10.1090/S0002-9947-1943-0009962-7 R. Baer The decomposition of enumerable, primary abelian groups into direct summands, Quart. J. Math. Oxford Ser. vol. 6 (1935) pp. 217-221.
- Reinhold Baer, Groups without proper isomorphic quotient groups, Bull. Amer. Math. Soc. 50 (1944), 267–278. MR 9955, DOI 10.1090/S0002-9904-1944-08134-2
- Reinhold Baer, The homomorphism theorems for loops, Amer. J. Math. 67 (1945), 450–460. MR 12302, DOI 10.2307/2371960
- Reinhold Baer, Splitting endomorphisms, Trans. Amer. Math. Soc. 61 (1947), 508–516. MR 20561, DOI 10.1090/S0002-9947-1947-0020561-7
- Reinhold Baer, Endomorphism rings of operator loops, Trans. Amer. Math. Soc. 61 (1947), 517–529. MR 20562, DOI 10.1090/S0002-9947-1947-0020562-9
- Reinhold Baer, The double chain condition in cyclic operator groups, Amer. J. Math. 69 (1947), 37–45. MR 19613, DOI 10.2307/2371652
- Ross A. Beaumont, Groups with isomorphic proper subgroups, Bull. Amer. Math. Soc. 51 (1945), 381–387. MR 12294, DOI 10.1090/S0002-9904-1945-08359-1
- R. H. Bruck, Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245–354. MR 17288, DOI 10.1090/S0002-9947-1946-0017288-3 I. S. Cohen Groups and rings of finite rank, Bull. Amer. Math. Soc. Abstract 52-5-110.
- Hans Fitting, Über die direkten Produktzerlegungen einer Gruppe in direkt unzerlegbare Faktoren, Math. Z. 39 (1935), no. 1, 16–30 (German). MR 1545486, DOI 10.1007/BF01201342
- O. N. Golowin, On factors without centres in direct decompositions of groups, Rec. Math. N. S. [Mat. Sbornik] 6(48) (1939), 423–426 (Russian, with English summary). MR 0001558
- Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601 B. Jónsson and A. Tarski On direct products of algebras, Bull. Amer. Math. Soc. Abstract 51-9-149. —A generalization of Wedderburn’s theorem, Bull. Amer. Math. Soc. Abstract 51-9-150.
- Irving Kaplansky, A note on groups without isomorphic subgroups, Bull. Amer. Math. Soc. 51 (1945), 529–530. MR 12267, DOI 10.1090/S0002-9904-1945-08382-7 V. Kořínek Sur la décomposition d’un groupe en produit direct des sousgroupes, Ćasopis pro pěstování matematiky a fysiky vol. 66 (1937) pp. 261-286.
- W. Krull, Über verallgemeinerte endliche Abelsche Gruppen, Math. Z. 23 (1925), no. 1, 161–196 (German). MR 1544736, DOI 10.1007/BF01506226 —Matrizen, Moduln und verallgemeinerte Abelsche Gruppen im Bereich der ganzen algebraischen Zahlen, Sitzungsberichte der Heidelberger Akademie der Wissenschaften, mathematisch-naturwissenschaftliche Klasse, 1932, pp. 13-38.
- Alexander Kurosch, Zur Zerlegung unendlicher Gruppen, Math. Ann. 106 (1932), no. 1, 107–113 (German). MR 1512752, DOI 10.1007/BF01455880
- A. Kurosch, Isomorphisms of direct decompositions, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 7 (1943), 185–202 (Russian, with English summary). MR 0011300
- A. Kurosh, Isomorphisms of direct decompositions. II, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 10 (1946), 47–72 (Russian, with English summary). MR 0018633
- Oystein Ore, Direct decompositions, Duke Math. J. 2 (1936), no. 3, 581–596. MR 1545950, DOI 10.1215/S0012-7094-36-00250-8 R. Remak Über die Zerlegungen der endlichen Gruppen in direkte unzerlegbare Faktoren, J. Reine Angew. Math. vol. 139 (1911) pp. 293-308.
- Otto Schmidt, Über unendliche Gruppen mit endlicher Kette, Math. Z. 29 (1929), no. 1, 34–41 (German). MR 1544991, DOI 10.1007/BF01180517
- M. F. Smiley, An application of lattice theory to quasigroups, Bull. Amer. Math. Soc. 50 (1944), 782–786. MR 11312, DOI 10.1090/S0002-9904-1944-08237-2
- J. H. Maclagan-Wedderburn, On the direct product in the theory of finite groups, Ann. of Math. (2) 10 (1909), no. 4, 173–176. MR 1502387, DOI 10.2307/1967406 H. Zassenhaus Lehrbuch der Gruppentheorie. I, Hamburger Mathematische Einzelschriften, vol. 21, 1937.
Additional Information
- © Copyright 1947 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 62 (1947), 62-98
- MSC: Primary 20.0X
- DOI: https://doi.org/10.1090/S0002-9947-1947-0021947-7
- MathSciNet review: 0021947