It is shown that every commutative arithmetic ring R has lambda-dimension less than or equal to 3. An example of a commutative Kaplansky ring with lambda-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self fp-injective, zero-Krull dimensional, CF or FSI then lambda-dim(R) less than or equal to 2. It is also shown that every zero-Krull dimensional commutative arithmetic ring is a Kaplansky ring and an adequate ring, that every Bezout ring with compact minimal prime spectrum is Hermite and-that each Bezout fractionnally self fp-injective ring is a Kaplansky ring. References: 19
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