References
Abian, A.: Direct product decompositions of commutative semisimple rings. Proc. Amer. Math. Soc.24, 502–507 (1970)
Abian, A.: Direct-sum decomposition of atomic and orthogonally complete rings. J. Austral. Math. Soc.11, 357–361 (1970)
Amitsur, S.A.: Generalized polynomial identities and pivotial monomials. Trans. Amer. Math. Soc.114, 210–226 (1965)
Amitsur, S.A.: On rings of quotients. Istituto Nazionale di Alta Matematica. Symposia Mathematica8, 149–164 (1972). London-New York: Academic Press 1972
Atiyah, M.F., Macdonald, I.G.: Introduction to commutative algebra. Reading, Mass.: Addison-Wesley 1969
Armendariz, E.P., Fisher, J.W., Steinberg, S.A.: Central localization of regular rings. Proc. Amer. Math. Soc.46, 315–321 (1974)
Beidar, K.I.: Rings with generalized identities. In: Procedings of the Third Allunion Symposium on Rings, Modules and Algebras (Tartu 1976), pp. 12–13
Beidar, K.I.: Rings with generalized identities I. Vestnik Moskov. Univ. Ser I Mat. Meh. (Engl. Transl.: Moscow Univ. Math. Bull.)2, 19–26 (1977)
Beidar, K.I.: Rings with generalized identities II. Vestnik Moskov. Univ. Ser I Mat. Meh. (Engl. Transl.: Moscow Univ. Math. Bull.)3, 30–37 (1977)
Beidar, K.I.: Semiprime rings with generalized identity, Uspehi Mat. Nauk.32, 249–250 (1977)
Beidar, K.I.: Rings of quotients of semiprime rings. Vestnik Moskov. Univ. Ser I. Mat. Meh. (Engl. Transl.: Moscow Univ. Math. Bull.)5, 36–43 (1978)
Bourbaki, N.: Eléments de Mathématique. Algèbre. Paris: Hermann, 1958, 1959, 1964
Burgess, W.D., Raphael, R.: Abian's order relation and orthogonal completeness for reduced rings, Pacific J. Math.54, 55–64 (1974)
Burgess, W.D., Raphael, R.: Complete and orthogonally complete rings. Canad. J. Math. (to appear)
Chacron, M.: Direct products of division rings and a paper of Abian. Proc. Amer. Math. Soc.29, 259–262 (1971)
Conrad, P.F.: The hulls of semiprime rings. Bull. Austral. Math. Soc.12, 311–314 (1975)
Dnestr booklet (open problems in ring theory and modules), second edition, Novosibirsk, 1976
Elizarov, V.P.: Strong torsion theories and filters, modules and rings of quotients. Sibirsk Math. Ž.14, 549–559 (1973)
Fisher, J.W.: Structure of semiprime PI-rings. Proc. Amer. Math. Soc.39, 465–467 (1973)
Fisher, J.W., Snider, R.L.: On the von Neumann regularity of rings with regular prime factor rings, Pacific J. Math.54, 135–144 (1974)
Jacobson, N.: Structure of rings. Revised. Colloquium Publications 37. Providence, R.I.: American Mathematical Society, 1956, 1964
Kharchenko, V.K.: Generalized identities with automorphisms. Algebra i Logika14, 215–237 (1975). Engl. Transl.: Algebra and Logic14, 132–148 (1975)
Kharchenko, V.K.: Invarint subrings of finite automorphism groups on semiprime rings. Algebra i Logika14, 328–344 (1975). Engl. Transl.: Algebra and Logic14, 203–213 (1975)
Kharchenko, V.K.: Generalized identities with automorphisms of associative rings with identity. Algebra i Logika14, 681–696 (1975). Engl. Transl.: Algebra and Logic14, 409–416 (1975)
Lambek, J.: On the structure of semiprime rings and their rings of quotients. Canad J. Math.13, 392–417 (1961)
Lambek, J.: Lectures on rings and modules. Waltham, Mass.: Blaisdell 1966
Lang, S.: Algebra, Reading, Mass.: Addison-Wesley 1965
Leron, U., Vapne, A.: Polynomial identities of related rings, Israel J. Math.8, 127–137 (1970)
Markov, V.T.: On rings of quotients of semiprime PI-rings and irreducible subdirect products, Uspehi Mat. Nauk,30, 253–254 (1975)
Markov, V.T.: A remark on Engel varieties of associative algebras with identity. In: Proceedings of the Fourteenth Allunion Conference in Algebra, vol. 2 (Novosibirsk 1977), pp. 54–55.
Martindale, W.S. III: Rings with involution and polynomial identities. J. Algebra11, 186–194 (1969)
Martindale, W.S. III: Prime rings satisfying a generalized polynomial identity. J. Algebra12 576–584 (1969)
Martindale, W.S. III: On semiprime PI-rings. Proc. Amer. Math. Soc.40, 365–369 (1973)
Montgomery, S.: A structure theorem and positive-definiteness condition in rings with involution. J. Algebra43, 181–192 (1976)
Raphael, R., Stephenson, W.: Orthogonally complete rings. Canad. Math. Bull.20, 347–351 (1977)
Rowen, L.H.: Rings with central polynomials, J. Algebra31, 187–222 (1974)
Rowen, L.H.: Structure of rings with involution applied to generalized polynomial identities. Canad. J. Math.27, 573–584 (1975)
Utumi, Y.: On quotient rings. Osaka Math. J.8, 1–18 (1956)
Wong, E.T., Johnson, R.E.: Self-injective rings. Canad Math. Bull.2, 167–173 (1959)
Zaharov, V.K.: Orthocompletion of modules, rings and Boolean algebras. In: Ordered sets and lattices vol. 4, pp. 54–66 Saratov University 1976
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Beidar, C.I., Mikhalev, A.V. & Salavova, C. Generalized identities and semiprime rings with involution. Math Z 178, 37–62 (1981). https://doi.org/10.1007/BF01218370
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01218370