Algebra i logika
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Algebra Logika: Year: Volume: Issue: Page: Find

 Algebra Logika, 2004, Volume 43, Number 4, Pages 482–505 (Mi al86)

Varieties of Associative Algebras Satisfying Engel Identities

O. B. Finogenova

Ural State University

Abstract: A variety of associative algebras (rings) is said to be Engel if it satisfies an identity of the form $[\ldots[[x,y],y],\ldots,y]=0$. On the Zorn lemma, every non-Engel variety contains some just non-Engel variety, that is, a minimal (w.r.t. inclusion) element in the set of all non-Engel varieties. A list of such varieties for algebras over a field of characteristic 0 was made up by Yu. N. Mal'tsev. Here, we present a complete description of just non-Engel varieties both for the case of algebras over a field of positive characteristic and for the case of rings. This gives the answer to Question 3.53 in the Dniester Notebook.

Keywords: Engel identity, just non-Engel variety, variety of associative rings, associative algebra over a field

Full text: PDF file (256 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2004, 43:4, 271–284

Bibliographic databases:

UDC: 512.552.4

Citation: O. B. Finogenova, “Varieties of Associative Algebras Satisfying Engel Identities”, Algebra Logika, 43:4 (2004), 482–505; Algebra and Logic, 43:4 (2004), 271–284

Citation in format AMSBIB
\Bibitem{Fin04} \by O.~B.~Finogenova \paper Varieties of Associative Algebras Satisfying Engel Identities \jour Algebra Logika \yr 2004 \vol 43 \issue 4 \pages 482--505 \mathnet{http://mi.mathnet.ru/al86} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2105850} \zmath{https://zbmath.org/?q=an:1065.16019} \transl \jour Algebra and Logic \yr 2004 \vol 43 \issue 4 \pages 271--284 \crossref{https://doi.org/10.1023/B:ALLO.0000035118.51742.41} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249093859} 

• http://mi.mathnet.ru/eng/al86
• http://mi.mathnet.ru/eng/al/v43/i4/p482

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. R. Chekhlov, “Torsion-Free Weakly Transitive $E$-Engel Abelian Groups”, Math. Notes, 94:4 (2013), 583–589
2. O. B. Finogenova, “Almost commutative varieties of associative rings and algebras over a finite field”, Algebra and Logic, 52:6 (2014), 484–510
3. O. B. Finogenova, “Pochti lievo nilpotentnye mnogoobraziya assotsiativnykh kolets”, Sib. elektron. matem. izv., 12 (2015), 901–909
4. O. B. Finogenova, “Pochti lievo nilpotentnye nepervichnye mnogoobraziya assotsiativnykh algebr”, Tr. IMM UrO RAN, 21, no. 4, 2015, 282–291
5. Jespers E., Riley D., Shahada M., “Multiplicatively Collapsing and Rewritable Algebras”, Proc. Amer. Math. Soc., 143:10 (2015), PII S0002-9939(2015)12563-4, 4223–4236
6. Finogenova O.B., “Varieties Satisfying Semigroup Identities: Algebras Over a Finite Field and Rings”, Int. J. Algebr. Comput., 26:5 (2016), 985–1017
7. Riley D.M., “When Is a Power of the Frobenius Map on a Noncommutative Ring a Homomorphism?”, J. Algebra, 479 (2017), 159–172
8. A. V. Kislitsin, “On nonnilpotent almost commutative $L$-varieties of vector spaces”, Siberian Math. J., 59:3 (2018), 458–462
9. A. V. Kislitsin, “The Specht property of $L$-varieties of vector spaces over an arbitrary field”, Algebra and Logic, 57:5 (2018), 360–367
•  Number of views: This page: 264 Full text: 99 References: 35 First page: 1