Injective objects in the category of 𝑝-rings

Haines, David C.

doi:10.1090/S0002-9939-1974-0325490-9

Injective objects in the category of $p$-rings
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Proc. Amer. Math. Soc. 42 (1974), 57-60 Request permission

Abstract:

A p-ring (or generalized Boolean ring) P is a ring of fixed prime characteristic p in which ${a^p} = a$ for all a in P. In this paper P is partially ordered by a relation which is a generalization of the usual Boolean order. A subset S of P is then called quasiorthogonal if $ab(a - b) = 0$ for all a, b in S. It is shown that P is injective in the category of p-rings if and only if every quasiorthogonal subset has a supremum under this partial order.

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