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- W2115955963 abstract "A completely primary finite ring is a ring R with identity 1 ≠ 0 whose subset of all its zero-divisors forms the unique maximal ideal J. Let R be a commutative completely primary finite ring with the unique maximal ideal J such that J3 = (0) and J2 ≠ (0). Then R/J ≒ GF(ργ) and the characteristic of R is ργ, where 1 ≤ k ≤ 3, forsome prime ρ and positive integer γ. Let Ro = GR(pkr, pk) be a Galoissubring of R and let the annihilator of J be J2 so that R = Ro ⊕U ⊕V , where U and V are finitely generated Ro-modules. Let non-gativeintegers s and t be numbers of elements in the generating sets for U and V , respectively. When s = 2, t = 1 and the characteristic of R is p2 and p3; and when s = 2, t = 2 and the characteristic of R is p, the structure of the group of units R* of the ring R and its generators have been determined; these depend on the structural matrices (alij) and onthe parameters p, k, r, s and t." @default.
- W2115955963 created "2016-06-24" @default.
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- W2115955963 date "2005-01-01" @default.
- W2115955963 modified "2023-09-28" @default.
- W2115955963 title "Unit Groups of a Certain Class of Completely Primary Finite Rings" @default.
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