The Λ - Dimension of Commutative Arithmetic Rings
نویسنده
چکیده
It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky ring and an adequate ring, that every Bézout ring with compact minimal prime spectrum is Hermite and that each Bézout fractionnally self f p-injective ring is a Kaplansky ring.
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