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Transactions of the American Mathematical Society

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On chain varieties of linear algebras


Author: V. A. Artamonov
Journal: Trans. Amer. Math. Soc. 221 (1976), 323-338
MSC: Primary 17A99
DOI: https://doi.org/10.1090/S0002-9947-1976-0409572-5
MathSciNet review: 0409572
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Abstract: In the present paper we study varieties of linear k-algebras over a commutative associative Noetherian ring k with 1, whose subvarieties form a chain. We describe these varieties in terms of identities in the following cases: residually nilpotent varieties, varieties of alternative, Jordan and $ ( - 1,1)$-algebras.


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  • [1] V. A. Artamonov, Chain varieties of linear algebras, Trudy Moskov. Mat. Obšč. 29 (1973), 51-77 = Trans. Moscow Math. Soc. 29 (1973), 49-76. MR 0412242 (54:369)
  • [2] -, On varieties of restricted Lie algebras, Sibirsk. Mat. Ž. 6 (1974), 1197-1212. MR 0374208 (51:10408)
  • [3] S. Fajtlowicz, H. Subramanian and T. R. Sundaraman, Equationally precomplete rings, Notices Amer. Math. Soc. 18 (1971), 630. Abstract #71T-A119.
  • [4] T. R. Sundaraman, Lattice of precomplete varieties of rings, Indag. Math. 37 (1975), 144. MR 0371951 (51:8168)
  • [5] I. V. L'vov, On varieties of associative rings. I, Algebra i Logika 12 (1973), 269-297 = Algebra and Logic 12 (1973), 150-167. MR 0389973 (52:10802)
  • [6] M. Osborn, Varieties of algebras, Advances in Math. 8 (1972), 163-370. MR 0289587 (44:6775)
  • [7] M. Nagata, Local rings, Interscience Tracts in Pure and Appl. Math., no. 13, Interscience, New York, 1962. MR 27 #5790. MR 0155856 (27:5790)
  • [8] V. A. Artamonov, On finite algebras of prime dimension with no proper subalgebras, J. Algebra (to appear). MR 0419549 (54:7570)
  • [9] R. D. Schafer, An introduction to nonassociative algebras, Pure and Appl. Math., vol. 22, Academic Press, New York and London, 1966. MR 35 #1643. MR 0210757 (35:1643)
  • [10] K. McCrimmon, Alternative algebras satisfying polynomial identities, J. Algebra 24 (1973), 283-292. MR 47 #298. MR 0311736 (47:298)
  • [11] N. Jacobson, Structure of rings, 2nd ed., Amer. Math. Soc. Colloq. Publ., vol. 37, Amer. Math. Soc., Providence, R. I., 1964. MR 36 #5158. MR 0222106 (36:5158)
  • [12] K. McCrimmon, Finite power-associative division rings, Proc. Amer. Math. Soc. 17 (1966), 1173-1177. MR 34 #4319. MR 0204479 (34:4319)
  • [13] A. A. Nikitin, Almost alternative algebras, Algebra i Logika 13 (1974), 501-533. (Russian) MR 0393142 (52:13952)
  • [14] K. A. Zevlakov and I. P. Shestakov, On local finiteness in sense of Shirshov, Algebra i Logika 12 (1973), 41-73. (Russian) MR 0399188 (53:3039)
  • [15] A. I. Širšov, On some non-associative nil-rings and algebraic algebras, Mat. Sb. 41 (83) (1957), 381-394. (Russian) MR 19, 727. MR 0089841 (19:727h)

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DOI: https://doi.org/10.1090/S0002-9947-1976-0409572-5
Article copyright: © Copyright 1976 American Mathematical Society

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