PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2010 | 30 | 1 | 119-132
Tytuł artykułu

A reduction theorem for ring varieties whose subvariety lattice is distributive

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.
Rocznik
Tom
30
Numer
1
Strony
119-132
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-05-01
poprawiono
2009-11-04
Twórcy
  • Faculty of Mathematics and Mechanics, Ural State University, Lenina 51, 620083 Ekaterinburg, Russia
Bibliografia
  • [1] D.S. Ananichev, Almost distributive varieties of Lie rings, Mat. Sbornik 186 (4) (1995), 3-20 [Russian; Engl. translation Sbornik: Math. 186 (4) (1995), 465-483].
  • [2] V.A. Artamonov, On chain varieties of linear algebras, Trans. Am. Math. Soc. 221 (1976), 323-338. doi: 10.1090/S0002-9947-1976-0409572-5
  • [3] V.A. Artamonov, Lattices of varieties of linear algebras, Uspekhi Mat. Nauk 33 (2) (1978) 135-167 [Russian; Engl. translation Russ. Math. Surv. 33 (2) (1978), 155-193].
  • [4] G. Grätzer, General lattice theory, 2nd ed., Birkhäuser Verlag, Basel 1998.
  • [5] A.I. Mal'tsev, On a multiplication of classes of algebraic systems, Sib. Mat. Zh. 8 (2) (1967), 346-365 [Russian; Engl. translation Sib. Math. J. 8 (1967), 254-267]. doi: 10.1007/BF02302476
  • [6] Yu.N. Mal'tsev, On distributive varieties of associative algebras, in Investigations in the Theory of Rings, Algebras and Modules (Mat. Issledovaniya, Kishinev 76) (1984), 73-98 [Russian].
  • [7] M.V. Volkov, Lattices of varieties of algebras, Mat. Sbornik 109 (1) (1979) 60-79 [Russian; Engl. translation Math. USSR, Sbornik 37 (1) (1980), 53-69].
  • [8] M.V. Volkov, Periodic varieties of associative rings, Izvestiya VUZ. Matematika no.8 (1979) 3-13 [Russian; Engl. translation Soviet Math., Izv. VUZ 23 (8) (1979), 1-12].
  • [9] M.V. Volkov, Identities in lattices of ring varieties, Algebra Universalis 23 (1986), 32-43. doi: 10.1007/BF01190909
  • [10] M.V. Volkov and A.G. Geĭn, Identities of almost nilpotent Lie rings, Mat. Sbornik 118 (1) (1982), 132-142 [Russian; Engl. translation Math. USSR, Sbornik 46 (1) (1983), 133-142].
  • [11] E.I. Zel'manov, On Engel Lie algebras, Sibirsk. Mat. Zh 26 (5) (1988), 112-117 [Russian; Engl. translation Siberian Math. J. 29 (5) (1988), 777-781].
  • [12] K.A. Zhevlakov, A.M. Slinko, I.P. Shestakov and A.I. Shirshov, Rings that are nearly associative, Academic Press, New York 1982.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1165
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.