JUST NON COMMUTATIVE VARIETIES OF OPERATOR ALGEBRAS AND RINGS WITH SOME CONDITIONS ON NILPOTENT ELEMENTS

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Published: Mar 1, 1996
DOI: https://doi.org/10.5556/j.tkjm.27.1996.4362
Keywords:
Associative algebra variety of algebras polynomial identity Engel condition (identity) nilpotent element

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YURI N. MAL'CEV
Department of Mathematics, Altai State University, Barnaul, 656099, Russia; Departamento de Matematica, Universidade de Brasilia, 70919-Brasilia, DF. Brasil

Abstract




In §1 it is given a classification of Just noncommutative varieties of associative over algebras over commutative Jacobson ring with unity. In [1], [4] are given different proofs of the commutativity of a finite ring with central nilpotent elements. In §2 we give generalizations of these results for infinite rings and for the case of Engel identity.




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How to Cite
MAL’CEV, Y. N. (1996). JUST NON COMMUTATIVE VARIETIES OF OPERATOR ALGEBRAS AND RINGS WITH SOME CONDITIONS ON NILPOTENT ELEMENTS. Tamkang Journal of Mathematics, 27(1), 59–65. https://doi.org/10.5556/j.tkjm.27.1996.4362
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Vol. 27 No. 1 (1996)
Section
Papers
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References

I. N. Herstein, "A note on rings with central nilpotent elements," Proc. Amer. Math. Soc., 5(1954), 620.

H. Komatsu, H. Tominaga, "On noncommutative algebras and commutativity conditions," Resul­tate Math., 18(1990), 74-92.

H. Komatsu, H. Tominaga, "Commutative theorems for algebras and rings," Math. J. Okayama Univ., 33(1991), 71-95.

S. Ligh, "Finite rings with central nilpotent elements," Tamkang J. Math, 16(1985), 45-46

I L'vov, "On varieties of assoc1at1ve rings," Algebra i Logika, 12(1973), 269-297.

I. L'vov, Braun's theorem about the radical of finitely generated P.I.-algebras, Preprint N63, Inst. of Math., Novosibirk, 1984.

I. L'vov, "Locally weakly noetherian varieties of algebras," 3-th all Union conference on theory of rings, Tartu, USSR, 1976.

Y. Mal'cev, "Just noncommutative varieties of rings," Siberian J. Math, 17(1976), 1086-1096

Y. Mal'cev, "Just nonengelian locally finite varieties of rings," lzvestiya vuzov(MATEM.4TICA), 11(1982), 41-42.

Y. Mal'cev, "On the mathod of proving commutativity theorems for rings," Izvestia vuzov (MATEM.4TICA), 11(1985), 25-28

I. Rowen, Polynomial identities in ring theory, Academic Press, New-York 1980.

W. Streb, "Zur Structure wicht kommutativer ring," Math. J. Okayama Univ., 31(1989), 135-140.