Ternary Algebra

2004 ◽  
pp. 480-481
Author(s):  
Yolanda Lozano ◽  
Massimo Bianchi ◽  
Warren Siegel ◽  
Wiesław Dudek
Keyword(s):  
Ternary Algebra

scholarly journals Association schemes on triples and a ternary algebra

1990 ◽  
Vol 55 (2) ◽  
pp. 204-234 ◽  
Author(s):  
Dale M Mesner ◽  
Prabir Bhattacharya
Keyword(s):  
Association Schemes ◽  
Ternary Algebra

A NOTE ON HILBERT TERNARY ALGEBRAS

2009 ◽  
Vol 02 (03) ◽  
pp. 367-375 ◽  
Author(s):  
Fatemeh Bahmani
Keyword(s):  
Hilbert Spaces ◽  
Inner Product ◽  
Ternary Algebra ◽  
Positive Multiple ◽  
Ternary Algebras ◽  
Real Complex

We show that every simple abelian real Hilbert ternary algebra is isomorphic to the algebra of Hilbert-Schmidt operators between two real, complex or quaternionic Hilbert spaces, up to a positive multiple of the inner product.

FREE TERNARY ALGEBRAS

2000 ◽  
Vol 10 (06) ◽  
pp. 739-749 ◽  
Author(s):  
RAYMOND BALBES
Keyword(s):  
Distributive Lattice ◽  
Sufficient Conditions ◽  
Free Generator ◽  
Necessary And Sufficient Conditions ◽  
Finitely Generated ◽  
Bounded Distributive Lattice ◽  
Ternary Algebra ◽  
Free Generators ◽  
Ternary Algebras ◽  
Necessary And Sufficient

A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L. With this characterization, the free ternary algebra on one free generator is displayed. The poset of join irreducibles of finitely generated free ternary algebras is characterized. The uniqueness of the set of free generators and their pseudocomplements is also established.

A Characterization of Finite Ternary Algebras

1997 ◽  
Vol 07 (06) ◽  
pp. 713-721 ◽  
Author(s):  
J. A. Brzozowski ◽  
J. J. Lou ◽  
R. Negulescu
Keyword(s):  
Distributive Lattice ◽  
De Morgan Algebra ◽  
Ternary Algebra ◽  
Set Operations ◽  
Additional Constant ◽  
Ternary Algebras

A ternary algebra is a De Morgan algebra (that is, a distributive lattice with 0 and 1 and a complement operation that satisfies De Morgan's laws) with an additional constant Φ satisfying [Formula: see text], [Formula: see text], and [Formula: see text]. We provide a characterization of finite ternary algebras in terms of "subset-pair algebras," whose elements are pairs (X, Y) of subsets of a given base set ℰ, which have the property X ∪ Y = ℰ, and whose operations are based on common set operations.

INVOLUTED SEMILATTICES AND UNCERTAINTY IN TERNARY ALGEBRAS

2004 ◽  
Vol 14 (03) ◽  
pp. 295-310 ◽  
Author(s):  
J. A. BRZOZOWSKI
Keyword(s):  
Binary Operation ◽  
De Morgan Algebra ◽  
Ternary Algebra ◽  
Ternary Algebras ◽  
Ordered Pairs

An involuted semilattice <S,∨,-> is a semilattice <S,∨> with an involution-: S→S, i.e., <S,∨,-> satisfies [Formula: see text], and [Formula: see text]. In this paper we study the properties of such semilattices. In particular, we characterize free involuted semilattices in terms of ordered pairs of subsets of a set. An involuted semilattice <S,∨,-,1> with greatest element 1 is said to be complemented if it satisfies a∨ā=1. We also characterize free complemented semilattices. We next show that complemented semilattices are related to ternary algebras. A ternary algebra <T,+,*,-,0,ϕ,1> is a de Morgan algebra with a third constant ϕ satisfying [Formula: see text], and (a+ā)+ϕ=a+ā. If we define a third binary operation ∨ on T as a∨b=a*b+(a+b)*ϕ, then <T,∨,-,ϕ> is a complemented semilattice.

scholarly journals A Ternary Algebra Arising from Association Schemes on Triples

1994 ◽  
Vol 164 (3) ◽  
pp. 595-613 ◽  
Author(s):  
D.M. Mesner ◽  
P. Bhattacharya
Keyword(s):  
Association Schemes ◽  
Ternary Algebra
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