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Literature cited
D. Zelinsky, "Raising idempotents," Duke Math. J.,21, 315–322 (1954).
V. M. Kurochkin, "Splitting an algebra into a semidirect sum of a radical and a semi-simple subalgebra," Uch. Zap. Mosk. Gos. Univ. (MGU), Ser. Mat.,148, No. 4, 192–203 (1951).
Lyu Shao-Syue, "Decomposition of infinite algebras," Mat. Sb.,42, No. 3, 327–352 (1957).
V. A. Andrunakievich, V. I. Arnautov, and M. I. Ursul "Wedderburn decomposition of hereditarily linearly compact rings," Mat. Issled.,9, No. 1, 3–16 (1974).
G. Azumaya, "On maximally central algebras," Nagoya Math. J.,2, 119–150 (1951).
W. C. Brown, "A Wedderburn theorem for alternative algebras with identity over commutative rings," Trans. Am. Math. Soc.,182, 144–159 (1973).
V. N. Zhelyabin, "Theorem on splitting off the radical for alternative algebras over a local Hensel ring," Algebra Logika,18, No. 1, 81–90 (1980).
V. N. Zhelyabin, "Theorem on splitting off the radical for Jordan algebras over a local Hensel ring," Trudy Inst. Mat. Sib. Otdel. Akad. Nauk SSSR,4, 5–28 (1984).
Z. S. Lipkina, "Structure of compact rings," Sib. Mat. Zh.,14, No. 6, 1346–1348 (1973); No. 5, 1162–1163 (1979).
N. Bourbaki, General Topology, Topological Groups. Real Numbers and Groups and Spaces Connected with Them [Russian translation], Nauka, Moscow (1969).
N. Bourbaki, General Topology. Fundamental Structures [Russian translation], Nauka, Moscow (1968).
L. A. Skornyakov, "Locally bicompact biregular rings," Mat. Sb.,62, No. 1, 3–13 (1963).
A. M. Slin'ko, "Modules and representations of unassociative topological compact rings," Mat. Zametki,39, No. 6, 791–797 (1986).
A. M. Slin'ko, "Nonassociative compact rings," Algebra Logika,22, No. 3, 308–315 (1983).
A. M. Slin'ko, "Locally compact alternative and Jordan rings," Algebra Logika,25, No. 4, 436–444 (1986).
K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, and A. I. Shirshov, Nearly Associative Rings [in Russian], Nauka, Moscow (1978).
A. M. Slin'ko, "Structure of alternative and Jordan compact rings," Mat. Sb.,129, No. 3, 378–385 (1986).
O. Zariski and P. Samuel, Commutative Algebra [Russian translation], Vol. 2, IL, Moscow (1963).
N. Jacobson, Structure of Representations and Jordan Algebras, Am. Math. Soc., Providence (1968).
K. A. Zhevlakov and I. P. Shestakov, "Local finiteness in the sense of Shirshov," Algebra Logika,12, No. 3, 41–73 (1973).
J. Milnor and d. Husemoller, Symmetric Bilinear Forms [Russian translation], Nauka, Moscow (1986).
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Translated from Algebra i Logika, Vol. 27, No. 3, pp. 359–372, May–June, 1988.
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Slin'ko, A.M. Decomposition of a compact ring into the sum of the radical and an inertial subring. Algebra and Logic 27, 225–233 (1988). https://doi.org/10.1007/BF01978568
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DOI: https://doi.org/10.1007/BF01978568