# zbMATH — the first resource for mathematics

$$p$$-rings and their boolean-vector representation. (English) Zbl 0044.26202

##### Keywords:
rings, modules, fields
Full Text:
##### References:
 [1] A. L. Foster,The n-ality theory of rings, Proc. of the Nat’l. Acad. of Sc., Vol 35 (1949). pp. 31–38. · Zbl 0031.25004 [2] ,The idempotent elements of a commutative ring form a Boolean algebra; ring dualityand transformation theory, Duke Math. J., Vol 13 (1946), pp. 247–258. · Zbl 0060.06604 [3] ,The theory of Boolean-like rings, Trans. of the Amer. Math. Soc., Vol 59 (1946), pp.166–187. · Zbl 0060.06605 [4] ,On the n-ality theories in rings and their logical algebras, including tri-ality principle in three-valued logics, Amer. Journal of Math., Vol 72, No 1 (1950), pp. 101–123. · Zbl 0037.01801 [5] A. L. Foster,On the permutational representation of general sets of operations by partition lattices, Trans. of the Amer. Math. Soc., July, 1949. · Zbl 0037.01704 [6] , andB. A. Bernstein,A dual-symmetric-definition of field, Amer. Journal of Math., Vol 67 (1945), pp. 329–349. · Zbl 0060.06602 [7] ,Symmetric approach to commutative rings, with duality theorem: Boolean duality as special case, Duke Math. Journal, Vol. 11 (1944), pp. 603–616. · Zbl 0060.06601 [8] N. H. Mc Coy andDeane Montgomery,A representation of generalized Boolean rings, Duke Math. Journal, Vol. 3 (1937), pp. 455–459. · Zbl 0017.24402 [9] M. H. Stone,The theory of representations for Boolean algebras, Trans. of the Amer. Math. Soc., Vol. 40 (1936), pp. 37–111. · Zbl 0014.34002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.