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Generalized identities and semiprime rings with involution

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References

  1. Abian, A.: Direct product decompositions of commutative semisimple rings. Proc. Amer. Math. Soc.24, 502–507 (1970)

    Google Scholar 

  2. Abian, A.: Direct-sum decomposition of atomic and orthogonally complete rings. J. Austral. Math. Soc.11, 357–361 (1970)

    Google Scholar 

  3. Amitsur, S.A.: Generalized polynomial identities and pivotial monomials. Trans. Amer. Math. Soc.114, 210–226 (1965)

    Google Scholar 

  4. Amitsur, S.A.: On rings of quotients. Istituto Nazionale di Alta Matematica. Symposia Mathematica8, 149–164 (1972). London-New York: Academic Press 1972

    Google Scholar 

  5. Atiyah, M.F., Macdonald, I.G.: Introduction to commutative algebra. Reading, Mass.: Addison-Wesley 1969

    Google Scholar 

  6. Armendariz, E.P., Fisher, J.W., Steinberg, S.A.: Central localization of regular rings. Proc. Amer. Math. Soc.46, 315–321 (1974)

    Google Scholar 

  7. Beidar, K.I.: Rings with generalized identities. In: Procedings of the Third Allunion Symposium on Rings, Modules and Algebras (Tartu 1976), pp. 12–13

  8. 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)

    Google Scholar 

  9. 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)

    Google Scholar 

  10. Beidar, K.I.: Semiprime rings with generalized identity, Uspehi Mat. Nauk.32, 249–250 (1977)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. Bourbaki, N.: Eléments de Mathématique. Algèbre. Paris: Hermann, 1958, 1959, 1964

    Google Scholar 

  13. Burgess, W.D., Raphael, R.: Abian's order relation and orthogonal completeness for reduced rings, Pacific J. Math.54, 55–64 (1974)

    Google Scholar 

  14. Burgess, W.D., Raphael, R.: Complete and orthogonally complete rings. Canad. J. Math. (to appear)

  15. Chacron, M.: Direct products of division rings and a paper of Abian. Proc. Amer. Math. Soc.29, 259–262 (1971)

    Google Scholar 

  16. Conrad, P.F.: The hulls of semiprime rings. Bull. Austral. Math. Soc.12, 311–314 (1975)

    Google Scholar 

  17. Dnestr booklet (open problems in ring theory and modules), second edition, Novosibirsk, 1976

  18. Elizarov, V.P.: Strong torsion theories and filters, modules and rings of quotients. Sibirsk Math. Ž.14, 549–559 (1973)

    Google Scholar 

  19. Fisher, J.W.: Structure of semiprime PI-rings. Proc. Amer. Math. Soc.39, 465–467 (1973)

    Google Scholar 

  20. 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)

    Google Scholar 

  21. Jacobson, N.: Structure of rings. Revised. Colloquium Publications 37. Providence, R.I.: American Mathematical Society, 1956, 1964

    Google Scholar 

  22. Kharchenko, V.K.: Generalized identities with automorphisms. Algebra i Logika14, 215–237 (1975). Engl. Transl.: Algebra and Logic14, 132–148 (1975)

    Google Scholar 

  23. 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)

    Google Scholar 

  24. 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)

    Google Scholar 

  25. Lambek, J.: On the structure of semiprime rings and their rings of quotients. Canad J. Math.13, 392–417 (1961)

    Google Scholar 

  26. Lambek, J.: Lectures on rings and modules. Waltham, Mass.: Blaisdell 1966

    Google Scholar 

  27. Lang, S.: Algebra, Reading, Mass.: Addison-Wesley 1965

    Google Scholar 

  28. Leron, U., Vapne, A.: Polynomial identities of related rings, Israel J. Math.8, 127–137 (1970)

    Google Scholar 

  29. Markov, V.T.: On rings of quotients of semiprime PI-rings and irreducible subdirect products, Uspehi Mat. Nauk,30, 253–254 (1975)

    Google Scholar 

  30. 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.

  31. Martindale, W.S. III: Rings with involution and polynomial identities. J. Algebra11, 186–194 (1969)

    Google Scholar 

  32. Martindale, W.S. III: Prime rings satisfying a generalized polynomial identity. J. Algebra12 576–584 (1969)

    Google Scholar 

  33. Martindale, W.S. III: On semiprime PI-rings. Proc. Amer. Math. Soc.40, 365–369 (1973)

    Google Scholar 

  34. Montgomery, S.: A structure theorem and positive-definiteness condition in rings with involution. J. Algebra43, 181–192 (1976)

    Google Scholar 

  35. Raphael, R., Stephenson, W.: Orthogonally complete rings. Canad. Math. Bull.20, 347–351 (1977)

    Google Scholar 

  36. Rowen, L.H.: Rings with central polynomials, J. Algebra31, 187–222 (1974)

    Google Scholar 

  37. Rowen, L.H.: Structure of rings with involution applied to generalized polynomial identities. Canad. J. Math.27, 573–584 (1975)

    Google Scholar 

  38. Utumi, Y.: On quotient rings. Osaka Math. J.8, 1–18 (1956)

    Google Scholar 

  39. Wong, E.T., Johnson, R.E.: Self-injective rings. Canad Math. Bull.2, 167–173 (1959)

    Google Scholar 

  40. Zaharov, V.K.: Orthocompletion of modules, rings and Boolean algebras. In: Ordered sets and lattices vol. 4, pp. 54–66 Saratov University 1976

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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

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