On algebraic subrings of rings of continuous functions
DOI:
https://doi.org/10.24193/subbmath.2026.3.1Keywords:
Algebraic subring, absolutely convex subring, saturated subring, rings of continuous functions, weakly algebraic subringAbstract
A subring S of C(X) is called algebraic if it satisfies the following conditions: R⊆S, and for all f ∈ C(X), if f2 ∈ S, then f ∈ S. This notion of algebraic subrings is further explored and characterized in the paper. Moreover, the paper provides examples to illustrate the results and introduces two generalizations of algebraic subrings, which are examined in detail.
Mathematics Subject Classification (2010): 13A99, 54C40.
Received 30 December 2025; Accepted 29 May 2026.
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