Results 11 to 20 of about 154,127 (212)

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This 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.
europepmc   +2 more sources

Topological spectrum of elements in topological algebras; pp. 271–281 [PDF]

Proceedings of the Estonian Academy of Sciences, 2018
Properties of the sets of left, right, and two-sided topologically quasi-invertible elements, topological spectra, and topological spectral radii of elements in (not necessarily unital or commutative) topological algebras are studied.
Mati Abel, Yuliana de Jesús Zárate-Rodríguez   +1 more
doaj   +1 more source

Topological Hochschild cohomology and generalized Morita equivalence [PDF]

, 2004
We explore two constructions in homotopy category with algebraic precursors in the theory of noncommutative rings and homological algebra, namely the Hochschild cohomology of ring spectra and Morita theory.
Andrew Baker, Andrey Lazarev, Generalized Morita Equivalence   +2 more
core   +3 more sources

Topological UP-algebras

Discussiones Mathematicae - General Algebra and Applications, 2019
In this paper, we introduce the notion of topological UP-algebras and several types of subsets of topological UP-algebras, and prove the generalization of these subsets. We also introduce the notions of quotient topological spaces of topological UP-algebras and topological UP-homomorphisms.
Satirad Akarachai, Iampan Aiyared
openaire   +2 more sources

On the topological product of galbed algebras [PDF]

Proceedings of the Estonian Academy of Sciences
We generalize some results about the topological product and the topological projective limit of galbed algebras. We also prove that the topological product is an (αn)-galbed algebra if and only if its each factor is an (αn)-galbed algebra.
Mart Abel
doaj   +1 more source

Constructive algebraic topology

Bulletin des Sciences Mathématiques, 2002
The classical ``computation'' methods in Algebraic Topology most often work by means of highly infinite objects and in fact +are_not+ constructive. Typical examples are shown to describe the nature of the problem. The Rubio-Sergeraert solution for Constructive Algebraic Topology is recalled.
Rubio, J., Sergeraert, F.
openaire   +6 more sources

On the Wielandt and Bhatt-Dedania Theorems [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
In this paper, we generalize a norm topology in Wielandt’s theorem for unital normed algebras and in Bhatt-Dedania’s theorem for Banach algebras, with each element being a zero topological divisor, by using 2-normed algebra and 2-Banach ...
Ekram Abdullah, Marwan A. Jardo, Amir Mohammed   +2 more
doaj   +1 more source

A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube [PDF]

, 2013
We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\lambda_s$ (the algebraic convergence) and $\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively.
Aleksandar Pavlović, B. Balcar, B. Balcar, B. Balcar, B. Balcar, B. Velickovic, D. Maharam, E. K. Douwen van, I. Farah, K. Kunen, M. S. Kurilić, M. S. Kurilić, M. S. Kurilić, M. S. Kurilić, M. Talagrand, M. Talagrand, Miloš S. Kurilić, R. Engelking, S. Todorcevic, T. Jech   +19 more
core   +2 more sources

Weakly topologized algebras [PDF]

Proceedings of the American Mathematical Society, 1957
Let E be an algebra over the reals or complex numbers, E' a total subspace of the algebraic dual of E, o(E, E') the weak topology defined on E by E'. In Theorems 1 and 2 of [2], the author established necessary and sufficient conditions for E, equipped with topology o-(E, E'), to be a locally m-convex algebra and to be a topological algebra.
openaire   +2 more sources

Double multipliers on topological algebras

International Journal of Mathematics and Mathematical Sciences, 1999
The main purpose of this paper is to investigate some topological properties of the double multiplier algebra on a topological algebra. Let Md(A) be the double multiplier algebra on a topological algebra A, and let u and s be the uniform and strong ...
L. A. Khan, N. Mohammad, A. B. Thaheem
doaj   +1 more source