ternary ring
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2018 ◽  
Vol 106 (2) ◽  
pp. 184-199
Author(s):  
ROBERT S. COULTER

We revisit the coordinatisation method for projective planes by considering the consequences of using finite fields to coordinatise projective planes of prime power order. This leads to some general restrictions on the form of the resulting planar ternary ring (PTR) when viewed as a trivariate polynomial over the field. We also consider how the Lenz–Barlotti type of the plane being coordinatised impacts the form of the PTR polynomial, thereby deriving further restrictions.


2015 ◽  
Vol 61 (5) ◽  
pp. 2942-2951 ◽  
Author(s):  
Dingyi Pei ◽  
Zhiqiang Lin ◽  
Xiaolei Zhang

2013 ◽  
Vol 57 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Dennis Bohle ◽  
Wend Werner

AbstractWe associate to every JB*-triple system a so-called universal enveloping ternary ring of operators (TRO). We compute the universal enveloping TROs of the finite dimensional Cartan factors.


2013 ◽  
Vol 155 (3) ◽  
pp. 475-482 ◽  
Author(s):  
PEKKA SALMI ◽  
ADAM SKALSKI

AbstractIt is shown that if T is a ternary ring of operators (TRO), X is a nondegenerate sub-TRO of T and there exists a contractive idempotent surjective map P: T → X then P has a unique, explicitly described extension to a conditional expectation between the associated linking algebras. A version of the result for W*-TROs is also presented and some applications mentioned.


2012 ◽  
Vol 20 (2) ◽  
pp. 159-170
Author(s):  
Lászlo L. Stachó ◽  
Wend Werner

Abstract The purpose of the following is to try to make sense of the stereo- graphic projection in a non-commutative setup. To this end, we consider the open unit ball of a ternary ring of operators, which naturally comes equipped with a non-commutative version of a hyperbolic metric and ask for a manifold onto which the open unit ball can be mapped so that one might think of this situation as providing a noncommutative analog to mapping the open disk of complex numbers onto the hyperboloid in three space, equipped with the restriction of the Minkowskian metric. We also obtain a related result on the Jordan algebra of self-adjoint operators


2009 ◽  
Vol 61 (6) ◽  
pp. 1262-1278
Author(s):  
Z. Dong

Abstract In this paper, we mainly study operator spaces which have the locally lifting property (LLP). The dual of any ternary ring of operators is shown to satisfy the strongly local reflexivity, and this is used to prove that strongly local reflexivity holds also for operator spaces which have the LLP. Several homological characterizations of the LLP and weak expectation property are given. We also prove that for any operator space V, V** has the LLP if and only if V has the LLP and V* is exact.


1998 ◽  
Vol 61 (1-2) ◽  
pp. 17-31 ◽  
Author(s):  
Walter Benz ◽  
Khuloud Ghalieh

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