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On generating free products of lattices

Authors: G. Grätzer and J. Sichler
Journal: Proc. Amer. Math. Soc. 46 (1974), 9-14
MSC: Primary 06A20
MathSciNet review: 0344167
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Abstract: For a lattice $ K$ let $ g(K)$ denote the cardinality of the smallest generating set of $ K$. Let $ L$ be the free product of the lattices $ A$ and $ B$. It is proved that $ g(L) = g(A) + g(B)$. This is proved, in fact, for free products with respect to any given equational class of lattices. Some applications and generalizations are also given.

References [Enhancements On Off] (What's this?)

  • [1] G. Grätzer, Lattice theory: First concepts and distributive lattices, Freeman, San Francisco, Calif., 1971. MR 0321817 (48:184)
  • [2] G. Grätzer, H. Lakser and C. R. Platt, Free products of lattices, Fund. Math. 69 (1970), 233-240. MR 43 #116. MR 0274351 (43:116)
  • [3] G. Grätzer and J. Sichler, Free decompositions of a lattice, Canad. J. Math. (to appear). MR 0369195 (51:5430)
  • [4] B. Jónsson, Relatively free products of lattices, Algebra Universalis 1 (1971/72), 362-373. MR 46 #106. MR 0300946 (46:106)

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Keywords: Lattice, free product, generating set
Article copyright: © Copyright 1974 American Mathematical Society

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