منابع مشابه
Representations of Relatively Complemented Modular Lattices
Introduction. A module over a ring will be said to be locally projective if and only if every finitely generated submodule is projective. As will be shown (7.14), it readily follows from known facts that if M is a locally projective module over a regular ring R, then the set L(M, R) of all finitely generated submodules of M is a relatively complemented modular lattice. This paper is concerned w...
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A sublattice in a lattice is called supermodular if, for every two elements, one of which belongs to the sublattice, at least one of their meet and join also belongs to the sublattice. In this note, we describe supermodular sublattices in products of relatively complemented lattices.
متن کاملComplemented modular lattices with involution and Orthogonal Geometry
We associate with each orthogeometry (P,⊥) a CMIL, i.e. a complemented modular lattice with involution, L(P,⊥) consisting of all subspaces X and X with dimX < א0 and study its rôle in decompositions of (P,⊥) as directed resp. disjoint union. We also establish a 1-1-correspondence between ∃-varieties V of CMILs with V generated by its finite dimensional members and ‘quasivarieties’ G of orthogeo...
متن کاملOn perfect pairs for quadruples in complemented modular lattices and concepts of perfect elements
Gel’fand and Ponomarev [11] introduced the concept of perfect elements and constructed such in the free modular lattice on 4 generators. We present an alternative construction of such elements u (linearly equivalent to theirs) and for each u a direct decomposition u, u of the generating quadruple within the free complemented modular lattice on 4 generators u, u are said to form a perfect pair. ...
متن کاملBalanced D-lattices Are Complemented *
We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1940
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1940-07133-2