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Full Exposition of Specht's Problem

Belov-Kanel, Alexei;  Rowen, Louis;  Vishne, Uzi — 2012

Serdica Mathematical Journal

2010 Mathematics Subject Classification: Primary: 16R10; Secondary: 16R30, 17A01, 17B01, 17C05. This paper combines [15], [16], [17], and [18] to provide a detailed sketch of Belov’s solution of Specht’s problem for affine algebras over an arbitrary commutative Noetherian ring, together with a discussion of the general setting of Specht’s problem in universal algebra and some applications to the structure of T-ideals. Some illustrative examples are collected along the way.

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.

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