Results 221 to 230 of about 36,818 (256)
Journal of Mathematical Sciences, 2023 AbstractThe extremal structure of zero-neighbourhoods of a topological module is analyzed reaching unexpected conclusions when the module topology is not Hausdorff. These results motivate us to introduce the notion of metric modules, which are modules endowed with a translation-invariant metric, turning them into an (additive) topological group.
Francisco Javier García-Pacheco
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Topological Bicomplex Modules [PDF]
Advances in Applied Clifford Algebras, 2016 In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski functionals in bicomplex modules. We also study the conditions under which topological bicomplex modules and locally bicomplex convex modules become hyperbolic normable and ...
Romesh Kumar
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Spectral Topology on MV-Modules [PDF]
New Mathematics and Natural Computation, 2015 In this paper, the spectral topology and quasi-spectral topology of proper prime A-ideals in an MV-module are introduced. We show that the spectral topology of proper ⋅-prime ideals of a PMV-algebra with unity for product, is the same as the spectral topology of proper prime ideals in an MV-algebra.
Fereshteh Forouzesh +2 more
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On topological M-injective modules
Topology and its Applications, 2023A topological module \(U\) over a topological ring \(R\) is called topological injective if for every topological \(R\)-module \(M\), every open submodule \(K\) of \(M\), every continuous monomorphism \(f:K\rightarrow M\) and every continuous homomorphism \(g:K\rightarrow U\), there exists a continuous homomorphism \(h:M\rightarrow U\) such that \(hf=g\
Yunita Septriana Anwar +3 more
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Mathematical Notes, 2003
Let \(k\) be a division ring with an absolute value \(|\cdot|\) and \(\tau\) the topology on \(k\) generated by \(|\cdot|\). For a vector \(k\)-space \(V\) and a fixed linear base \(X\) of \(V\) a \((k,\tau)\)-space topology \(\tau_b\) on \(V\) is defined as follows: A base at \(0\) for \(\tau_b\) consists of subsets \(U(f):=\sum_{x\in X}U_{f(x)}x ...
Arnautov, V. I., Filippov, K. M.
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Let \(k\) be a division ring with an absolute value \(|\cdot|\) and \(\tau\) the topology on \(k\) generated by \(|\cdot|\). For a vector \(k\)-space \(V\) and a fixed linear base \(X\) of \(V\) a \((k,\tau)\)-space topology \(\tau_b\) on \(V\) is defined as follows: A base at \(0\) for \(\tau_b\) consists of subsets \(U(f):=\sum_{x\in X}U_{f(x)}x ...
Arnautov, V. I., Filippov, K. M.
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On the lattice of linear module topologies
Communications in Algebra, 1993We study various features of the lattice LM of linear module topologies on a module M and their impact on the structure of the abstract module. A particular emphasis is given to: a) permanence properties of 1- minimal topologies (=atoms in the subset of LM of Hausdorff topologies) in analogy with the theory of minimal topological groups; b) the usual ...
DIKRANJAN, Dikran, Tonolo A.
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Zariski topology on lattice modules
Asian-European Journal of Mathematics, 2015Let [Formula: see text] be a lattice module over a [Formula: see text]-lattice [Formula: see text] and [Formula: see text] be the set of all prime elements in lattice modules [Formula: see text]. In this paper, we study the generalization of the Zariski topology of multiplicative lattices [N. K. Thakare, C. S. Manjarekar and S.
Ballal, Sachin, Kharat, Vilas
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Linear topologies and sequential compactness in topological modules
Quaestiones Mathematicae, 2017We prove that an absolute semi-valued ring is rst-countable if the set of invertibles is separable and its closure contains 0. We also show that every linearly topologized topological module over an absolute semi-valued ring whose invertibles approach 0 has the trivial topology.
Francisco Javier García-Pacheco
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Characterization of χ-Topological Modules
2014In this paper, we attempt to study the topological notions of multiplication module in the realm of purity. We let χ denote a collection of multiplication ideals of a ring R. We call an R module M to be χ-topological module (the topology being the Zariski topology on the prime spectrum of M) if, together with all the axiom of a topological space, it ...
Saugata Purkayastha, Helen K. Saikia
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