The diamond lemma for ring theory

Advances in Mathematics - Tập 29 - Trang 178-218 - 1978
George M Bergman1
1Department of Mathematics, University of California, Berkeley, California 94720, USA

Tài liệu tham khảo

1963, 70, 335 Amitsur, 1974, Polynomial identities, Israel J. Math., 19, 183, 10.1007/BF02756631 Bergman, 1971, The index of a group in a semigroup, Pacific J. Math., 36, 55, 10.2140/pjm.1971.36.55 Bergman, 1974, Modules over coproducts of rings, Trans. Amer. Math. Soc., 200, 1, 10.1090/S0002-9947-1974-0357502-5 Bergman, 1974, Coproducts, and some universal ring constructions, Trans. Amer. Math. Soc., 200, 33, 10.1090/S0002-9947-1974-0357503-7 G. M. Bergman, Some category-theoretic ideas in algebra, in “Proceedings of the 1974 (Vancouver) I.C.M.,” Vol. 1, pp. 285–296. Bergman, 1976, Rational relations and rational identities in division rings, J. Algebra, 43, 252, 10.1016/0021-8693(76)90159-9 Bergman, 1976, Rational relations and rational identities in division rings, J. Algebra, 43, 267, 10.1016/0021-8693(76)90160-5 Bergman, 1974, General theory of algebraic structures, Course notes G. M. Bergman, A lemma of Razmyslov, and central polynomials, unpublished. G. M. Bergman and A. P. Doohovskoy, On subsemigroups of free semigroups, and quasivarieties, in preparation. Birkhoff, 1937, Representability of Lie algebras and Lie groups by matrices, Ann. of Math., 38, 526, 10.2307/1968569 Bokut', 1972, Unsolvability of the word problem, and subalgebras of finitely presented Lie algebras, Izv. Akad. Nauk S.S.S.R. Ser. Mat., 36, 1173 P. M. Cohn, Homomorphic images of special Jordan-algebras, in “Proceedings of the 1954 (Amsterdam) I.C.M.” Cohn, 1959, On the free product of associative rings, Math. Z., 71, 380, 10.1007/BF01181410 Cohn, 1960, On the free product of associative rings. II. The case of skew fields, Math. Z., 73, 433, 10.1007/BF01215516 Cohn, 1965 Cohn, 1966, Some remarks on the invariant basis property, Topology, 5, 215, 10.1016/0040-9383(66)90006-1 Cohn, 1968, On the free product of associative rings, III, J. Algebra, 8, 376, 10.1016/0021-8693(68)90066-5 1968, Erratum, 10, 123 Cohn, 1969, Dependence in rings. II. The dependence number, Trans. Amer. Math. Soc., 135, 267 Cohn, 1971 Dean, 1956, Completely free lattices generated by partially ordered sets, Trans. Amer. Math. Soc., 83, 238, 10.1090/S0002-9947-1956-0080076-2 Dicks, 1977, Mayer-Vietoris presentations over colimits of trees of rings, Proc. London Math. Soc., 34, 557, 10.1112/plms/s3-34.3.557 1961, Vol. II Evans, 1951, On multiplicative systems defined by generators and relations. I. Normal form theorems, 47, 637 Evans, 1963, A decision problem for transformations of trees, Canad. J. Math., 15, 584, 10.4153/CJM-1963-059-9 Evans, 1963, The isomorphism problem for some classes of multiplicative systems, Trans. Amer. Math. Soc., 109, 303, 10.1090/S0002-9947-1963-0153727-5 Gluhov, 1960, On the problem of isomorphism of lattices, Dokl. Akad. Nauk S.S.S.R., 132, 254 1960, Soviet Math. Dokl., 1, 519 Hall, 1958, Some word problems, J. London Math. Soc., 33, 482, 10.1112/jlms/s1-33.4.482 Hermann, 1926, Die Frage der endlich viele Schritte in der Theorie der Polynomideale, Math. Ann., 95, 31, 10.1007/BF01206635 Hughes, 1973, Projective Planes Jacobson, 1962 Jacobson, 1968, Structure and Representation of Jordan Algebras, Vol. 39 Jónsson, 1954, Modular lattices and Desargues' theorem, Math. Scand., 2, 295, 10.7146/math.scand.a-10416 Knuth, 1969, Simple word problems in universal algebras, 263 Kurosh, 1960 Lawvere, 1963, Functional Semantics of Algebraic Theories Leavitt, 1957, Modules without invariant basis number, 8, 322 Linton, 1966, Some aspects of equational categories, 88 MacLane, 1971, Categories for the Working Mathematician Mal'cev, 1973, Algebraic Systems, Band 192 Mauldon, 1964, Nonorthogonal idempotents whose sum is idempotent, Amer. Math. Monthly, 71, 963, 10.2307/2311910 Milnor, 1965, On the structure of Hopf algebras, Ann. Of Math., 81, 211, 10.2307/1970615 Newman, 1942, On theories with a combinatorial definition of “equivalence”, Ann. of Math., 43, 223, 10.2307/1968867 Ore, 1933, Theory of noncommutative polynomials, Ann. of Math., 34, 480, 10.2307/1968173 Osborne, 1972, Varieties of algebras, Advances in Math., 8, 163, 10.1016/0001-8708(72)90003-5 D. Pigozzi, Universal equational theories and varieties of algebra, to appear. Poincaré, 1900, Sur les groupes continus, Trans. Cambridge Philos. Soc., 18, 220 Razmyslov, 1973, The finite generability of the identities of a matrix algebra of order 2 over a field of characteristic 0, Algebra i Logika, 12, 83, 10.1007/BF02218641 Regev, 1977, The T-ideal generated by the standard identity 3[x1, x2, x3], Israel J. Math., 26, 10.1007/BF03007662 Rosset, 1975, A new proof of the Amitsur-Levitski identity, Israel J. Math., 23, 187, 10.1007/BF02756797 Seidenberg, 1971, On the length of a Hilbert ascending chain, 29, 443 Serre, 1965 Shay, 1971, Discoherently associative bifunctors on groups Stallings, 1965, Whitehead torsion of free products, Ann. of Math., 82, 354, 10.2307/1970647 Taft, 1975, Hopf algebras with nonsemisimple antipode, 49, 269 Radford, 1977, Operators on Hopf algebras, Amer. J. Math., 99, 139, 10.2307/2374012 Viennot, 1974, Algèbres de Lie libres et monoïdes libres van der Waerden, 1948, Free products of groups, Amer. J. Math., 70, 527, 10.2307/2372196 Whitman, 1941, Free lattices, Ann. of Math., 42, 325, 10.2307/1969001 Whitman, 1942, Free lattices, Ann. of Math., 43, 104, 10.2307/1968883 Witt, 1937, Treue Darstellung Liescher Ringe, J. Reine Angew. Math., 117, 152, 10.1515/crll.1937.177.152 Birkhoff, 1967, Lattice Theory Jacobson, 1975, PI-Algebras, An Introduction Kostant, 1958, A theorem of Frobenius, a theorem of Amitsur-Levitzky, and cohomology theory, J. Math. Mech. (now Indian Univ. J. Math.), 7, 237, 10.1512/iumj.1958.7.57019 Mitchell, 1972, Rings with several objects, Advances in Math., 8, 1, 10.1016/0001-8708(72)90002-3 Procesi, 1976, The invariant theory of n × n matrices, Advances in Math., 19, 306, 10.1016/0001-8708(76)90027-X Gluhov, 1970, Lattice Theory (Russian, survey article) Evans, 1976, Some solvable word problems Pigozzi, 1976, Base-undecidable properties of universal varieties, Algebra Universalis, 6, 193, 10.1007/BF02485829 Crawley, 1973 Hutchinson, 1973, Recursively undecidable word problems of modular lattices and diagram chasing, J. Algebra, 26, 385, 10.1016/0021-8693(73)90001-X Hutchinson, 1977, Embedding and unsolvability theorems for modular lattices, Algebra Universalis, 7, 47, 10.1007/BF02485417 Regev, 1978, The representations of Sn and explicit identities for P.I. algebras, J. Algebra, 51, 25, 10.1016/0021-8693(78)90133-3 Corwin, 1975, Graded Lie algebras in mathematics and physics, Rev. Modern Physics, 47, 573, 10.1103/RevModPhys.47.573 G. M. Bergman The global dimension of mixed coproduct/tensor-product algebras, to appear. G. M. Bergman, Embedding filtered rings in completed graded rings, to appear. G. M. Bergman, The Lie algebra of vector fields on Rn satisfies polynomial identities, to appear. Cohn, 1977, Skew Field Constructions, 27 P. M. Cohn, The universal field of fractions of a semifir, Proceedings London Math. Soc., to appear.