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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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Commutative and Bounded BE-algebras [PDF]
Algebra, 2013 Summary: We introduce the notions of the commutative and bounded BE-Algebras. We give some related properties of them.
Zekiye Çiloğlu, Yılmaz Çeven
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Quasi-Commutative Algebras [PDF]
Applied Categorical Structures, 2008 We characterise algebras commutative with respect to a Yang-Baxter operator (quasi-commutative algebras) in terms of certain cosimplicial complexes. In some cases this characterisation allows the classification of all possible quasi-commutative structures.
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Division Algebras with Left Algebraic Commutators [PDF]
Algebras and Representation Theory, 2017 لنفترض أن D عبارة عن جبر قسمة مع المركز F و K a (ليس بالضرورة مركزيًا) من D. يسمى العنصر a D جبريًا يساريًا (جبريًا أيمنًا) على K، إذا كان هناك متعدد حدود أيسر غير صفري a 0 + a 1 x + i + a n x n (متعدد الحدود الأيمن resp. a 0 + x a 1 + i + x n a n ) على K بحيث يكون 0 + a 1 a + i + a n a n = 0 (resp. a 0 + a 1 + i + a n a n a n ).
Mehdi Aaghabali +2 more
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On the commutative algebra of categories [PDF]
Algebraic & Geometric Topology, 2018 51 pages; some proofs and notation clarified; this is the final version to appear in Algebraic and Geometric ...
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An algebraic model for commutative Hℤ–algebras [PDF]
Algebraic & Geometric Topology, 2017 We show that the homotopy category of commutative algebra spectra over the Eilenberg-Mac Lane spectrum of the integers is equivalent to the homotopy category of E-infinity-monoids in unbounded chain complexes. We do this by establishing a chain of Quillen equivalences between the corresponding model categories.
Richter, Birgit, Shipley, Brooke
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On commutativity of C*-algebras [PDF]
Glasgow Mathematical Journal, 1987 Two numerical characterizations of commutativity for C*-algebra (acting on the Hilbert space H) were given in [1]; one used the norms of self-adjoint operators in (Theorem 2), and the other the numerical index of (Theorem 3). In both cases the proofs were based on the result of Kaplansky which states that if the only nilpotent operator in is 0 ...
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Journal of Pure and Applied AlgebraLet $KQ$ be a path algebra, where $Q$ is a finite quiver and $K$ is a field. We study $KQ/C$ where $C$ is the two-sided ideal in $KQ$ generated by all differences of parallel paths in $Q$. We show that $KQ/C$ is always finite dimensional and its global dimension is finite.
Edward L. Green, Sibylle Schroll
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On the deformation of commutative algebras [PDF]
Transactions of the American Mathematical Society, 1969 Introduction. Given a field k and a k-algebra A, Gerstenhaber has introduced the concept of a deformation of A [8] which is a k[[t]]-algebra structure on the module A[[t]]. One of the main problems of the theory of deformations is to determine those algebras for which the only deformation (modulo an equivalence relation) is the usual k[[t]]-algebra ...
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Algebraic Dependence of Commuting Elements in Algebras [PDF]
, 2008 LaTeX, 14 pages, no ...
Silvestrov, Sergei +2 more
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