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Injective objects in the category of $ p$-rings


Author: David C. Haines
Journal: Proc. Amer. Math. Soc. 42 (1974), 57-60
MSC: Primary 06A70; Secondary 16A38
DOI: https://doi.org/10.1090/S0002-9939-1974-0325490-9
MathSciNet review: 0325490
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0325490-9
Keywords: Category of p-rings, p-rings, injectivity, Boolean rings
Article copyright: © Copyright 1974 American Mathematical Society

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