Lattices With Involution
نویسندگان
چکیده
منابع مشابه
Commutative integral bounded residuated lattices with an added involution
By a symmetric residuated lattice we understand an algebra A = (A,∨,∧, ∗,→,∼, 1, 0) such that (A,∨,∧, ∗,→, 1, 0) is a commutative integral bounded residuated lattice and the equations ∼∼ x = x and ∼ (x ∨ y) =∼ x∧ ∼ y are satisfied. The aim of the paper is to investigate properties of the unary operation ε defined by the prescription εx :=∼ x → 0. We give necessary and sufficient conditions for ...
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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...
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Let $R$ be a ring with involution $*$. An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$. The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.
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An infinte word w avoids a pattern p with the involution θ if there is no substitution for the variables in p and no involution θ such that the resulting word is a factor of w. We investigate the avoidance of patterns with respect to the size of the alphabet. For example, it is shown that the pattern α θ (α)α can be avoided over three letters but not two letters, whereas it is well known that α...
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We give a necessary and su¢ cient condition for a bounded involution lattice to be isomorphic to the direct square of its invariant part. This result is applied to show relations between related lattices of an algebra: For instance, generalizing some earlier results of G. Czédli and L. Szabó it is proved that any algebra admits a connected compatible partial order whenever its quasiorder lattic...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1958
ISSN: 0002-9947
DOI: 10.2307/1993112