Jacobson structure theory for Hestenes ternary rings
نویسندگان
چکیده
منابع مشابه
Distributive Lattices of Jacobson Rings
We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.
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Munn [11] proved that the Jacobson radical of a commutative semigroup ring is nil provided that the radical of the coefficient ring is nil. This was generalized, for semigroup algebras satisfying polynomial identities, by Okniński [14] (cf. [15, Chapter 21]), and for semigroup rings of commutative semigroups with Noetherian rings of coefficients, by Jespers [4]. It would be interesting to obtai...
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Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...
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1. Let T be a ternary ring with the ternary operation T(a, b, c) and the distinguished elements 0, 1 (see [4]). On T, two loop structures can be defined by means of the binary operations a+b = T(a, 1, b) and ab=T(a, b, 0). The resulting loops are called the additive and the multiplicative loop of Ty respectively. Together with a0 = 0a = 0 they define the structure of a double loop on T, which s...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1973-0335583-1