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Hedetniemi conjectured in 1966 that if G and H are finite graphs with chromatic number n, then the chromatic number of the direct product of G and H is also n. We mention two well‐known results pertaining to this conjecture and offer an improvement of the one, which partially proves the other. The first of these two results is due to Burr et al. (Ars Combin 1 (1976), 167–190), who showed that...
We study the class of rings in which every P-flat module is flat. In domains this property characterizes Prüfer domains. We investigate the preservation of this property under localization, homomorphic image, direct product, amalgamation, and trivial ring extension. Our results yield examples which enrich the current literature with new and original families of rings that satisfy this property.
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