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Semigroup rings in semisimple varieties

Published online by Cambridge University Press:  17 April 2009

A.V. Kelarev
Affiliation:
Department of MathematicsUniversity of Tasmania, GPO Box 252–37HobartTas. 7001Australia, e-mail: [email protected]
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Abstract

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We describe semigroup rings which belong to self-dual varieties generated by a finite number of finite fields.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Gardner, B.J., ‘Semi-simple radical classes of algebras and attainability of identities’, Pacific J. Math. 61 (1975), 401416.CrossRefGoogle Scholar
[2]Gardner, B.J., Osborn, J.M. and Shestakov, I., ‘Varieties and tensor products’, Nova J. Algebra Geometry 1 (1992), 347357.Google Scholar
[3]Gardner, B.J. and Stewart, P.N., ‘On semi-simple radical classes’, Bull. Austral. Math. Soc. 13 (1975), 349353.CrossRefGoogle Scholar
[4]Iskander, A.A., ‘Product of ring varieties and attainability’, Trans. Amer. Math. Soc. 193 (1974), 231238.CrossRefGoogle Scholar
[5]Martynov, L.M., ‘On decidable rings’, Math. Notes Ural State Univ. (Sverdlovsk) 8 (1973), 8293.Google Scholar
[6]McCoy, N.H., Rings and ideals, Carus Monographs Series 8 (Mathematical Society of America, 1948).CrossRefGoogle Scholar
[7]Michler, G. and Wille, R., ‘Die primitiven Klassen arithmetischer Ringe’, Math. Z. 113 (1970), 369372.CrossRefGoogle Scholar
[8]Okniński, J., Semigroup algebras (Marcel Dekker, New York, 1991).Google Scholar
[9]Shevrin, L.N. and Martynov, L.M., ‘On attainable classes of algebras’, Sibirsk. Mat. Zh. 12 (1971), 13631381.Google Scholar
[10]Snider, R.L., ‘Complemented hereditary radicals’, Bull. Austral. Math. Soc. 4 (1971), 307320.CrossRefGoogle Scholar
[11]Stewart, P.N., ‘Semi-simple radical classes’, Pacific J. Math. 32 (1970), 249254.CrossRefGoogle Scholar
[12]Sundararaman, T.R., ‘Lattice of precomplete varieties of rings’, Proc. Kon. Nederl. Akad. Wetensch. A78 (1975), 144148.CrossRefGoogle Scholar
[13]Vasantha, W.B., ‘A note on semigroup rings which are Boolean rings’, Sci. Phys. Sci. 3 (1991), 6768.Google Scholar
[14]Vernikov, B.M., ‘Self-dual varieties of associative rings’, Ural. Gos. Univ. Mat. Zap. 14 (1985), 3137.Google Scholar
[15]Volkov, M.V., ‘Varieties of associative rings with the property of embeddability of amalgams’, Mat. Zametki 33 (1983), 313.Google Scholar
[16]Volkov, M.V. and Kelarev, A.V., ‘Varieties and bands of associative algebras’, Izv. Vyssh. Uchebn. Zaved. Mat. (1986), 1623.Google Scholar
[17]Werner, H. and Wille, R., ‘Characterizierunger der primitiven Klassen arithmetischer Ringe’, Math. Z. 115 (1970), 197200.CrossRefGoogle Scholar
[18]Wiegandt, R., ‘Radical and semisimple classes of rings’, Queen's Papers in Pure and Appl. Math. 37 (Kingston, 1974).Google Scholar