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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 5, Pages 1042–1059 (Mi izv1506)  

This article is cited in 47 scientific papers (total in 47 papers)

Varieties and $Z_2$-graded algebras

A. R. Kemer


Abstract: A structure theory of varieties of associative algebras over a field of characteristic zero is constructed. It is shown that any variety is a product of a nilpotent and a semiprime variety. The semiprime varieties are described.
Bibliography: 10 titles.

Full text: PDF file (1662 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:2, 359–374

Bibliographic databases:

UDC: 512
MSC: Primary 16A48, 16A03; Secondary 16A22, 16A12
Received: 15.02.1982

Citation: A. R. Kemer, “Varieties and $Z_2$-graded algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 48:5 (1984), 1042–1059; Math. USSR-Izv., 25:2 (1985), 359–374

Citation in format AMSBIB
\Bibitem{Kem84}
\by A.~R.~Kemer
\paper Varieties and $Z_2$-graded algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 5
\pages 1042--1059
\mathnet{http://mi.mathnet.ru/izv1506}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=764308}
\zmath{https://zbmath.org/?q=an:0586.16010}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 2
\pages 359--374
\crossref{https://doi.org/10.1070/IM1985v025n02ABEH001285}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Allan Berele, “Cocharacters ofZ/2Z-graded algebras”, Isr J Math, 61:3 (1988), 225  crossref  mathscinet  zmath  isi
    2. Giulia Maria Piacentini Cattaneo, “Alcuni metodi computazionali in algebra”, Seminario Mat e Fis di Milano, 60:1 (1990), 223  crossref  zmath
    3. E. I. Zel'manov, I. P. Shestakov, “Prime alternative superalgebras and the nilpotence of the radical of a free alternative algebra”, Math. USSR-Izv., 37:1 (1991), 19–36  mathnet  crossref  mathscinet  zmath  adsnasa
    4. A. A. Zolotykh, “Trace identities of matrix superalgebras with an involution”, Math. USSR-Izv., 37:1 (1991), 37–68  mathnet  crossref  mathscinet  zmath  adsnasa
    5. Allan Berele, “Azumaya-like properties of verbally prime algebras”, Journal of Algebra, 133:2 (1990), 272  crossref
    6. Amitai Regev, “Tensor products of matrix algebras over the Grassmann algebra”, Journal of Algebra, 133:2 (1990), 512  crossref
    7. Jorn B Olsson, Amitai Regev, “Modular cocharacters for P.I. algebras”, Journal of Algebra, 143:1 (1991), 93  crossref
    8. Onofrio Mario Vincenzo, “On the graded identities ofM 1,1(E)”, Isr J Math, 80:3 (1992), 323  crossref  mathscinet  zmath  isi
    9. Allan Berele, “Generic verbally prime pi-algebras and their gk-dimensions”, Communications in Algebra, 21:5 (1993), 1487  crossref
    10. Allan Berele, “Classification theorems for verbally semiprime algebras”, Communications in Algebra, 21:5 (1993), 1505  crossref
    11. Luisa Carini, Drensky Vesselin, “Plethysmsfor representations of Lie superalgebras with applications to P. I algebras”, Linear and Multilinear Algebra, 37:4 (1994), 239  crossref
    12. Allan Berele, “Examples and counterexamples for M1,1 embeddings”, Journal of Algebra, 172:2 (1995), 379  crossref
    13. Onofrio Mario Di Vincenzo, “Cocharacters of g-graded algebras”, Communications in Algebra, 24:10 (1996), 3293  crossref
    14. Jenö Szigeti, “On the characteristic polynomial of supermatrices”, Isr J Math, 107:1 (1998), 229  crossref  mathscinet  zmath  isi
    15. D. I. Piontkovskii, “On Hilbert series and the homology of PI-algebras”, Sb. Math., 189:11 (1998), 1685–1700  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. A. Berele, A. Regev, “Codimensions of products and of intersections of verbally primeT-ideals”, Isr. J. Math, 103:1 (1998), 17  crossref
    17. Allan Berele, Louis Rowen, “T-Ideals and SuperAzumaya Algebras”, Journal of Algebra, 212:2 (1999), 703  crossref
    18. A. Ya. Belov, “Counterexamples to the Specht problem”, Sb. Math., 191:3 (2000), 329–340  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. V. V. Shchigolev, “The finite basis property of $T$-spaces over fields of characteristic zero”, Izv. Math., 65:5 (2001), 1041–1071  mathnet  crossref  crossref  mathscinet  zmath
    20. Shchigolev V.V., “On the stabilization problem for submodules of Specht modules”, Journal of Algebra, 251:2 (2002), 790–812  crossref  isi  elib
    21. O.M. Di Vincenzo, V. Drensky, V. Nardozza, “Subvarieties of the Varieties Generated by the SuperalgebraM1, 1(E) orM2(�)”, Communications in Algebra, 31:1 (2003), 437  crossref
    22. Daniela La Mattina, “On the graded identities and cocharacters of the algebra of 3×3 matrices”, Linear Algebra and its Applications, 384 (2004), 55  crossref
    23. Onofrio M. Di Vincenzo, Vincenzo Nardozza, “-graded cocharacters for superalgebras of triangular matrices”, Journal of Pure and Applied Algebra, 194:1-2 (2004), 193  crossref
    24. E. A. Kireeva, A. N. Krasilnikov, “On Some Extremal Varieties of Associative Algebras”, Math. Notes, 78:4 (2005), 503–517  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. Allan Berele, “Colength sequences for Kemer algebras”, Journal of Algebra, 293:1 (2005), 155  crossref
    26. A BERELE, “Asymptotics in the cocharacter sequence of A⊗BA⊗B”, Advances in Applied Mathematics, 37:2 (2006), 183  crossref  elib
    27. A. Ya. Belov, “Burnside-type problems, theorems on height, and independence”, J. Math. Sci., 156:2 (2009), 219–260  mathnet  crossref  mathscinet  zmath  elib  elib
    28. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    29. ONOFRIO M. DI VINCENZO, VINCENZO NARDOZZA, “GRADED POLYNOMIAL IDENTITIES OF VERBALLY PRIME ALGEBRAS”, J. Algebra Appl, 06:03 (2007), 385  crossref
    30. A. V. Grishin, L. M. Tsybulya, “On the structure of a relatively free Grassmann algebra”, J. Math. Sci., 171:2 (2010), 149–212  mathnet  crossref  mathscinet  elib
    31. Onofrio M. Di Vincenzo, Viviane Ribeiro Tomaz da Silva, “On -graded polynomial identities of the Grassmann algebra”, Linear Algebra and its Applications, 431:1-2 (2009), 56  crossref
    32. A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    33. Aljadeff E., Kanel-Belov A., “Representability and Specht problem for G-graded algebras”, Advances in Mathematics, 225:5 (2010), 2391–2428  crossref  isi
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    35. Onofrio M. Di Vincenzo, Plamen Koshlukov, “On the ∗-polynomial identities of M1,1(E)”, Journal of Pure and Applied Algebra, 215:3 (2011), 262  crossref
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    40. Di Vincenzo O.M., Nardozza V., “On the Existence of the Graded Exponent for Finite Dimensional Z(P)-Graded Algebras”, Can. Math. Bul.-Bul. Can. Math., 55:2 (2012), 271–284  crossref  isi
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