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𝒯 -semiring pairs

Jaiung Jun, Kalina Mincheva, Louis Rowen (2022)

Kybernetika

We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

Let R and S be commutative rings with unity, f : R → S a ring homomorphism and J an ideal of S . Then the subring R ⋈ f J : = { ( a , f ( a ) + j ) ∣ a ∈ R and j ∈ J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R ⋈ f J is a (generalized) filter ring.

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