: Astronomie: arithmetic ring

mathematical technique > algebra > commutative algebra > commutative ring > arithmetic ring

arithmetic ring

In algebra, a commutative ring R is said to be arithmetical (or arithmetic) if any of the following equivalent conditions hold : 1) The localization R_m of R at m is a uniserial ring for every maximal ideal m of R. 2) For all ideals a , b, and c, a ∩ (b+c) = (a ∩ b) + (a ∩ c) 3) For all ideals a , b, and c, a + (b ∩ c) = (a + b) ∩ (a + c) The last two conditions both say that the lattice of all ideals of R is distributive. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Arithmetical_ring)

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