2022/03/02 by Jun, Jaiung, Mincheva, Kalina, Rowen, Louis
#08A72 #12K10 #13C60 #14T10 #16Y60 #18A05 #18C10 #18E05 #20N20 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 08A05 #Rings and Algebras (math.RA) #Secondary 08A30
paper · doi:10.48550/arxiv.2203.01086
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.