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On the Hilbert Evolution Algebras of a Graph
Siberian Mathematical Journal, 2022A separable Hilbert evolution algebra is a separable Hilbert space \(\mathcal{A}\) endowed with an algebra structure so that there exists an orthonormal basis \(\{e_i\}_{i\in\mathbb{N}}\) such that \begin{itemize} \item[i)] \(e_ie_i=\sum_{k\in\mathbb{N}}c_{ki}e_k\), for some scalars \(\{c_{ik}\}_{k\in\mathbb{N}}\), and \(e_ie_j=0\), for all \(i,j\in ...
Vidal, S. J. +2 more
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Journal of Intelligent & Fuzzy Systems, 2015
In this paper, we first introduce the notion of Stonean implicative filter in Hilbert algebra and study it in detail. Finally, we introduce a Stonean Hilbert algebra and investigate its properties, we prove that, H is a Stonean Hilbert algebra if and only if the set of all regular elements of
Ali Soleimani Nasab +1 more
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In this paper, we first introduce the notion of Stonean implicative filter in Hilbert algebra and study it in detail. Finally, we introduce a Stonean Hilbert algebra and investigate its properties, we prove that, H is a Stonean Hilbert algebra if and only if the set of all regular elements of
Ali Soleimani Nasab +1 more
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On prelinear Hilbert algebras with successor
Fuzzy Sets and Systems, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
José Luis Castiglioni +1 more
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Studia Logica, 2010
In this paper we develop a theory of Bosbach and Riecan states on non-trivial Hilbert algebras.
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In this paper we develop a theory of Bosbach and Riecan states on non-trivial Hilbert algebras.
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Traces, bitraces and hilbert algebras
Periodica Mathematica Hungarica, 1991The author shows that a *-algebra \(A\) has a non-trivial trace if there is a *-homomorphism of \(A\) onto a non-zero Hilbert algebra \(K\), and conversely a non-trivial trace on a normed *-algebra \(A\) satisfying \(A^ 2\) is dense in \(A\) gives rise to a non-zero *-homomorphism of \(A\) onto a Hilbert algebra.
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A NOTE ON HILBERT TERNARY ALGEBRAS
Asian-European Journal of Mathematics, 2009We 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.
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Hilbert algebras of fractions and maximal Hilbert algebras of quotients
Kobe Journal of Mathematics, 1988Let (A,\(\to,1)\) be a bounded Hilbert algebra. Set \(x\vee y=x^*\to y\), where \(x^*=x\to 0\). A Hilbert algebra \(A'\) is called a Hilbert algebra of fractions of A, written \(A\leq A'\), iff A is a Hilbert subalgebra of \(A'\) and for every \(a',b',c'\in A'\), \(a'\neq b'\), there exists \(a\in A\) such that \(a\vee a'\neq a\vee b'\) and \(a\vee c ...
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On the Hilbert Series of Koszul Algebras
Functional Analysis and Its Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ISOMORPHISMS OF HILBERT TERNARY ALGEBRAS
Mathematical Proceedings of the Royal Irish Academy, 2011Let \((V, (\;|\;))\) be a real Hilbert space with a trilinear map \([\;,\;,\;]: V\times \times V \times V \to V\) satisfying \(([x,y,z] \mid u) = (x \mid [u,z,y]) = (z\mid [y,x,u])\) and \([x, y, [z, w, u] ] = [[x,y,z], w, u]\) for all \(x, y, z, u, w\in V\).
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Pure Hilbert Algebras with Infimum
Logic Journal of IGPL, 2007In [6], iH-algebras were introduced in order to indicate an equational version of the class of Hilbert algebras where each pair of elements has infimum. These authors also proved that this variety hasthe class of Curry's implicative semilattices ([9]) as a proper subvariety.
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