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A Property of the Weak Subalgebra Lattice for Algebras with Some Non-Equalities

  • 투고 : 2008.07.09
  • 심사 : 2009.10.09
  • 발행 : 2010.06.30

초록

Let A be a locally finite total algebra of finite type such that $k^A(a_1,\cdots,a_n)\;{\neq}\;a_i$ ai for every operation $k^A$, elements $a_1,\cdots,a_n$ an and $1\;\leq\;i\;\leq\;n$. We show that the weak subalgebra lattice of A uniquely determines its (strong) subalgebra lattice. More precisely, for any algebra B of the same finite type, if the weak subalgebra lattices of A and B are isomorphic, then their subalgebra lattices are also isomorphic. Moreover, B is also total and locally finite.

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참고문헌

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피인용 문헌

  1. A STRONG PROPERTY OF THE WEAK SUBALGEBRA LATTICE FOR LOCALLY FINITE ALGEBRAS OF FINITE TYPE vol.23, pp.01, 2013, https://doi.org/10.1142/S0218196712500762
  2. Subalgebra lattices of a partial unary algebra vol.45, pp.4, 2012, https://doi.org/10.1515/dema-2013-0416