p-rings and ring-logics
Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 5 (1951) no. 3-4, pp. 279-300. 
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     author = {Foster, Alfred L.},
     title = {$p$-rings and ring-logics},
     journal = {Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche},
     pages = {279--300},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 5},
     number = {3-4},
     year = {1951},
     mrnumber = {47625},
     zbl = {0044.26201},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1951_3_5_3-4_279_0/}
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Foster, Alfred L. $p$-rings and ring-logics. Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 5 (1951) no. 3-4, pp. 279-300. http://archive.numdam.org/item/ASNSP_1951_3_5_3-4_279_0/

1 A.L. Foster, « On n-ality theories in rings and their logical algebras, including tri-ality principle in three valued logics », Amer. Jour. of Math., V. LXXII, pp. 101-123. | MR | Zbl

2 A.L. Foster, « p-Rings and their Boolean vector representation » Acta Mathematica, Vol. 84 (1950), pp. 231-261. | MR | Zbl

3 A.L. Foster, « p Rings and ring-logics », University of Calif. publications in mathematics, Vol. 1: 10 (1951), pp. 385-396. | MR | Zbl

4 A.L. Foster, « Boolean-extensions and sub-direct ring powers », In process of publication.

5 N.H. M, « Subrings of direct sums », Amer. Jour. of Math., Vol. LX (1938), pp. 374-382. | JFM | Zbl

6 N.H. M and Deane Montgomery, « A representation of generalized Boolean rings », Duke Math. Jour., Vol. 3, (1937) pp. 455-459. | MR | Zbl

7 M.H. Stone, « The theory of representations of Boolean algebra », Trans. of the Amer Math. Soc., V. 40 (1936), pp. 37-111. | JFM | MR | Zbl

8 A.L. Foster, « The idempotent elements of a commutative ring form a Boolean algebra; ring duality and transformation theory », Duke Math. Jour., Vol. 12 (1945), pp. 143.152. | MR | Zbl