-graded polynomial identities for
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Onofrio Mario Di Vincenzo, Vincenzo Nardozza (2002)
Rendiconti del Seminario Matematico della Università di Padova
Ю.М. Рябухин, Р.С. Флоря (1984)
Matematiceskie issledovanija
Azevedo, Sergio (2003)
Serdica Mathematical Journal
2000 Mathematics Subject Classification: 16R10, 16R20, 16R50The algebra Mn(K) of the matrices n × n over a field K can be regarded as a Z-graded algebra. In this paper, it is proved that if K is an infinite field, all the Z-graded polynomial identities of Mn(K) follow from the identities: x = 0, |α(x)| ≥ n, xy = yx, α(x) = α(y) = 0, xyz = zyx, α(x) = −α(y) = α(z ), where α is the degree of the corresponding variable. This is a generalization of a result of Vasilovsky about the Z-graded identities...
Giambruno, A., Zaicev, M. (2000)
Serdica Mathematical Journal
∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.It was recently proved that any variety of associative algebras over a field of characteristic zero has an integral exponential growth. It is known that a variety V has polynomial growth if and only if V does not contain the Grassmann algebra and the algebra of 2 × 2 upper triangular matrices. It follows that any variety with overpolynomial growth has exponent at least...
Mohammad Ashraf (1995)
Archivum Mathematicum
Let be fixed positive integers, and let be a ring with unity in which for every in there exist integers such that either or for all . In the present paper it is shown that is commutative if it satisfies the property (i.e. for all implies ).
Vukman, Joso, Kosi-Ulbl, Irena (2005)
International Journal of Mathematics and Mathematical Sciences
Vincenzo De Filippis, M. S. Tammam El-Sayiad (2009)
Rendiconti del Seminario Matematico della Università di Padova
Barry J. Gardner (1979)
Commentationes Mathematicae Universitatis Carolinae
Abu-Khuzam, Hazar (1989)
International Journal of Mathematics and Mathematical Sciences
Mikhail V. Volkov (2010)
Discussiones Mathematicae - General Algebra and Applications
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.
Gupta, Vishnu (1994)
International Journal of Mathematics and Mathematical Sciences
De Filippis, Vincenzo (2005)
Mathematica Pannonica
Qing Deng (1995)
Collectanea Mathematica
Joso Vukman (1999)
Commentationes Mathematicae Universitatis Carolinae
The purpose of this paper is to prove the following result: Let be a -torsion free semiprime ring and let be an additive mapping, such that holds for all . In this case is left and right centralizer.
Vincenzo de Filippis, Giovanni Scudo, Mohammad S. Tammam El-Sayiad (2012)
Czechoslovak Mathematical Journal
Let be a prime ring of characteristic different from , the Utumi quotient ring of , the extended centroid of , a non-central Lie ideal of , a non-zero generalized derivation of . Suppose that for all , then one of the following holds: (1) there exists such that for all ; (2) satisfies the standard identity and there exist and such that for all . We also extend the result to the one-sided case. Finally, as an application we obtain some range inclusion results of...
Abujabal, H.A.S., Khan, M.S. (1990)
International Journal of Mathematics and Mathematical Sciences
Gérard Cauchon (1976)
Bulletin de la Société Mathématique de France
Mishchenko, S., Zaicev, M. (2000)
Serdica Mathematical Journal
This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128.We study the asymptotic behaviour of numerical characteristics of polynomial identities of Lie algebras over a field of characteristic 0. In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics for the colength of a product...
K.W. Roggenkamp, Jae Keol Park (1995)
Forum mathematicum
Szigeti, Jeno (2006)
Serdica Mathematical Journal
2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.For an n×n matrix A over an arbitrary unitary ring R, we obtain the following Cayley-Hamilton identity with right matrix coefficients: (λ0I+C0)+A(λ1I+C1)+… +An-1(λn-1I+Cn-1)+An (n!I+Cn) = 0, where λ0+λ1x+…+λn-1 xn-1+n!xn is the right characteristic polynomial of A in R[x], I ∈ Mn(R) is the identity matrix and the entries of the n×n matrices Ci, 0 ≤ i ≤ n are in [R,R]. If R is commutative, then C0 = C1 = … = Cn-1 = Cn = 0 and our...
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