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- Marina V. Semenova, Friedrich Wehrung
- IJAC
- 2004

For a partially ordered set P , let Co(P ) denote the lattice of all order-convex subsets of P . For a positive integer n, we denote by SUB(LO) (resp., SUB(n)) the class of all lattices that can be embedded into a lattice of the form ∏

- Marina V. Semenova, V. I. Tumanov
- 2002

For a partially ordered set P , we denote by Co(P ) the lattice of order-convex subsets of P . We find three new lattice identities, (S), (U), and (B), such that the following result holds: Theorem. Let L be a lattice. Then L embeds into some lattice of the form Co(P ) iff L satisfies (S), (U), and (B). Furthermore, if L has an embedding into some Co(P ),… (More)

- Marina V. Semenova, Friedrich Wehrung
- IJAC
- 2003

For a positive integer n, we denote by SUB (resp., SUBn) the class of all lattices that can be embedded into the lattice Co(P ) of all orderconvex subsets of a partially ordered set P (resp., P of length at most n). We prove the following results: (1) SUBn is a finitely based variety, for any n ≥ 1. (2) SUB2 is locally finite. (3) A finite atomistic lattice… (More)

For a left vector space V over a totally ordered division ring F, let Co(V ) denote the lattice of convex subsets of V . We prove that every lattice L can be embedded into Co(V ) for some left F-vector space V . Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional, and L embeds into a finite lower bounded lattice of the form… (More)

- Marina V. Semenova, Anna Zamojska-Dzienio
- IJAC
- 2007

- Marina V. Semenova, Anna Zamojska-Dzienio
- Order
- 2011

- Anvar M. Nurakunov, Marina V. Semenova, +6 authors A. V. Kravchenko
- 2012

This survey paper reviews some recent results related to various derived lattices connected with various types of classes of algebraic structures which were obtained by the authors.

- Marina V. Semenova, Anna Zamojska-Dzienio
- Order
- 2010

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