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Feebly Projectable Algebraic Frames and Multiplicative Filters of Ideals

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Abstract

In the article (Martinez and Zenk, Algebra Universalis, 50, 231–257, 2003.), the authors studied several conditions on an algebraic frame L. In particular, four properties called Reg(1), Reg(2), Reg(3), and Reg(4) were considered. There it was shown that Reg(3) is equivalent to the more familiar condition known as projectability. In this article we show that there is a nice property, which we call feebly projectable, that is between Reg(3) and Reg(4). In the main section of the article we apply our notions to the frame of multiplicative filters of ideals in a commutative ring with unit and give characterizations of several well-known classes of commutative rings.

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Authors and Affiliations

  1. Department of Mathematics, Midwestern State University, 3410 Taft Blvd., Wichita Falls, TX, 76308, USA

    Michelle L. Knox

  2. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Warren Wm. McGovern

Authors
  1. Michelle L. Knox
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  2. Warren Wm. McGovern
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Correspondence to Michelle L. Knox.

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Knox, M.L., McGovern, W.W. Feebly Projectable Algebraic Frames and Multiplicative Filters of Ideals. Appl Categor Struct 15, 3–17 (2007). https://doi.org/10.1007/s10485-006-9038-3

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  • DOI: https://doi.org/10.1007/s10485-006-9038-3

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