A General Theory of Almost Splitting Sets |
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Authors: | Jung Wook Lim |
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Institution: | 1. Department of Mathematics , Kyungpook National University , Daegu , South Korea jwlim@knu.ac.kr |
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Abstract: | Let * be a star-operation of finite type on an integral domain D. In this paper, we generalize and study the concept of almost splitting sets. We define a saturated multiplicative subset S of D to be an almost g*-splitting set of D if for each 0 ≠ d ∈ D, there exists an integer n = n(d) ≥1 such that d n = st for some s ∈ S and t ∈ D with (t, s′)* = D for all s′ ∈ S. Among other things, we prove that every saturated multiplicative subset of D is an almost g*-splitting set if and only if D is an almost weakly factorial domain (AWFD) with *-dim (D) = 1. We also give an example of an almost g*-splitting set which is not a g*-splitting set. |
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Keywords: | g*-splitting set" target="_blank">Almost g*-splitting set Almost weakly factorial domain *-Complement Star-operation of finite type |
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