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Applied Categorical Structures, 2011
Let \(\mathcal V\) be a variety of (universal) algebras. A subalgebra of \(A\in \mathcal V\) is \textit{normal} if it is the universe image under some morphism of the subalgebra generated by constants in the target. Consider \(\mathbb{C}_{\mathcal V}\) (or just \(\mathbb{C}\)), the free algebra in \(\mathcal V\) over the empty set (the initial algebra ...
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Let \(\mathcal V\) be a variety of (universal) algebras. A subalgebra of \(A\in \mathcal V\) is \textit{normal} if it is the universe image under some morphism of the subalgebra generated by constants in the target. Consider \(\mathbb{C}_{\mathcal V}\) (or just \(\mathbb{C}\)), the free algebra in \(\mathcal V\) over the empty set (the initial algebra ...
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COMPLETE SYSTEMS OF SUBALGEBRAS
International Journal of Algebra and Computation, 2003In the 1960s, G. Grätzer introduced the notion of the minimal extension property (MEP) of a finite sequence in order to investigate pn-sequences and free spectra of algebras. While there are many particular results on the MEP, stating that some sequences or families of sequences have the MEP, no general result has been obtained so far and the main ...
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Relatively Parametrizable Subalgebras
Applied Categorical Structures, 2000In a previous paper [``Parametrizable algebras'', J. Lond. Math. Soc., II. Ser. 8, 750-752 (1974; Zbl 0296.08018)], the author proved that a universal algebra \(A\) is parametrizable iff it is projective in the variety which \(A\) generates. Here, he does the same for \(k\)-parametrizability and \(k\)-projectivity.
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Embedding lattices of fuzzy subalgebras into lattices of crisp subalgebras
Information Sciences, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON SUBSPECTRA GENERATED IN SUBALGEBRAS
Bulletin of the London Mathematical Society, 2003The present paper deals with some properties of ideals in commutative Banach algebras. It is a continuation of the author's earlier investigations published in [Stud. Math. 142, 245--251 (2000; Zbl 1002.46031) and Bol. Soc. Mat. Mex. (3) 7, 117--121 (2001; Zbl 1041.46035)].
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Algebras and Representation Theory, 2005
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Semilattices of Definable Subalgebras
Algebra and Logic, 2005Summary: In issues bearing on the structure of universal algebras \(\mathcal A\), derived structures, such as automorphism groups \(\text{Aut}\,\mathcal A\), subalgebra lattices \(\text{Sub}\, \mathcal A\), congruence lattices \(\text{Con}\, \mathcal A\), etc., play an important part.
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Journal of Lie Theory, 2015
A pair of Lie algebras \((L,L_0)\) is called transitive if \(L_0\) does not contain any non-trivial ideal of \(L\). Let \(L_1=\{x\in L_0\mid [x,L]\subset L_0\}\). Then \(L_0\) is called an ample nonlinear subalgebra of \(L\) if \(L_1\neq\{0\}\) and \(L_0=N_L(L_1)\) (normalizer), and \(L_1\) is called the kernel of \(L_0\).
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A pair of Lie algebras \((L,L_0)\) is called transitive if \(L_0\) does not contain any non-trivial ideal of \(L\). Let \(L_1=\{x\in L_0\mid [x,L]\subset L_0\}\). Then \(L_0\) is called an ample nonlinear subalgebra of \(L\) if \(L_1\neq\{0\}\) and \(L_0=N_L(L_1)\) (normalizer), and \(L_1\) is called the kernel of \(L_0\).
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Minimal hermitian compact operators related to a C*-subalgebra of K(H)
Journal of Mathematical Analysis and Applications, 2022Jiang Lining
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