Function-Space Supertopological Rings: m-Topology, d-Boundedness and Radical Structure
Year: 2026
Type: article
Abstract: The theory of supertopological rings, based on D-supercontinuity, provides a natural framework for studying rings of functions that fail to be topological rings under classical continuity assumptions. In this paper we develop a detailed ring-theoretic analysis of subrings of RX endowed with the m-topology and introduce the notion of functional generation as the fundamental structural condition governing supertopological compatibility. We prove that a subring of RX admits a supertopological ring structure under the m-topology if and only if it is functionally generated, thereby establishing a sharp maximality criterion. The internal algebraic structure of such rings is studied in depth: ideals and their d-closures preserve functional generation, zero divisors form d-closed sets, and d-boundedness arises naturally from the function-space setting. Lattice-theoretic properties are established, showing closure under arbitrary intersections and failure under unions
Author: Bhaskar Vashishth
Institution: University of Delhi
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W7154632977
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