Abstract
In the article we show that the sum of two PI-rings is again a PI-ring.
Similar content being viewed by others
References
O. H. Kegel, “Zur Nilpotenz gewisser assoziativer Ringe,”Math. Ann.,149, 258–260 (1962/63).
L. A. Bokut', “Imbedding in simple associative algebras,”Algebra Logika,15, No. 2, 117–142 (1978).
M. Ferrero and E. R. Puczylowski, “On rings which are sums of two subrings,”Arch. Math.,53, 4–10 (1989).
A. V. Kelarev, “A sum of two locally nilpotent rings may be not nil,”Arch. Math.,60, 431–435 (1993).
E. R. Puczylowski, “Some questions concerning radicals of associative rings,” to appear.
Yu. Bahturin and A. Giambruno, “Identities of the sums of commutative subalgebras,” to appear.
Yu. Bahturin and O. H. Kegel, “Lie algebras which are universal sums of Abelian subalgebras,” to appear.
W. S. Martindale, “Prime rings satisfying a generalized polynomial identity,”J. Algebra,12, 576–584 (1969).
L. H. Rowen,Polynomial Identities in Ring Theory, Academic Press (1980).
K. I. Beidar, W. S. Martindale, and A. V. Mikhalev, “Lie isomorphisms in prime rings with involution,” to appear inJ. Algebra.
K. I. Beidar, A. V. Mikhalev, and A. M. Slin'ko, “A criterion for primeness of nondegenerate alternative and Jordan algebras,”Trudy Mosk. Mat. Obshch.,50, 130–137 (1987).
M. Cabrera Garcia and A. Rodriguez Palacios, “A characterization of the center of a nondegenerate Jordan algebra,”Commun. Algebra,21, No. 1, 359–369 (1993).
R. Baer,Linear Algebra and Projective Geometry, Academic Press (1952).
K. R. Goodearl,Von Neumann Regular Rings, Pitmann (1979).
J. Lambek,Lectures on Rings and Modules, Blaisdell (1966).
K. I. Beidar, “Rings with generalized identities. III,”Vestnik MGU, Ser. Mat. Mekh.,4, 66–73 (1978).
D. A. Suprunenko and R. I. Tyshkevich,Commutative Matrices, Academic Press (1968).
Additional information
Translated fromAlgebra i Logika, Vol. 34, No. 1, pp. 3–11, January–February, 1995.
Supported by the Russian Foundation for Fundamental Research, grant No. 93-011-01544.
Rights and permissions
About this article
Cite this article
Beidar, K.I., Mikhalev, A.V. Generalized polynomial identities and rings which are sums of two subrings. Algebr Logic 34, 1–5 (1995). https://doi.org/10.1007/BF00750549
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00750549