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Conditions for a universal mapping of algebras to be a monomorphism. (English) Zbl 0331.08004

MSC:

08Axx Algebraic structures
18B15 Embedding theorems, universal categories
18C10 Theories (e.g., algebraic theories), structure, and semantics
18C05 Equational categories
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
17B35 Universal enveloping (super)algebras
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
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References:

[1] Reinhold Baer, Free sums of groups and their generalizations. An analysis of the associative law, Amer. J. Math. 71 (1949), 706 – 742. · Zbl 0033.34504 · doi:10.2307/2372361
[2] George M. Bergman, The diamond lemma for ring theory, Adv. in Math. 29 (1978), no. 2, 178 – 218. · Zbl 0326.16019 · doi:10.1016/0001-8708(78)90010-5
[3] Garrett Birkhoff, Representability of Lie algebras and Lie groups by matrices, Ann. of Math. (2) 38 (1937), no. 2, 526 – 532. · JFM 63.0090.01 · doi:10.2307/1968569
[4] Saunders MacLane, Categories for the working mathematician, Springer-Verlag, New York-Berlin, 1971. Graduate Texts in Mathematics, Vol. 5. · Zbl 0232.18001
[5] Hanna Neumann, Generalized free products with amalgamated subgroups, Amer. J. Math. 70 (1948), 590 – 625. · Zbl 0032.10402 · doi:10.2307/2372201
[6] M. H. A. Newman, On theories with a combinatorial definition of ”equivalence.”, Ann. of Math. (2) 43 (1942), 223 – 243. · Zbl 0060.12501 · doi:10.2307/1968867
[7] Jean-Pierre Serre, Lie algebras and Lie groups, Lectures given at Harvard University, vol. 1964, W. A. Benjamin, Inc., New York-Amsterdam, 1965. · Zbl 0132.27803
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