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Feebly projectable algebraic frames and multiplicative filters of ideals. (English) Zbl 1119.06008

Summary: In the article [J. Martinez and E. R. Zenk, Algebra Univers. 50, 231–257 (2003; Zbl 1092.06011)], 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.

MSC:

06D22 Frames, locales
13A15 Ideals and multiplicative ideal theory in commutative rings

Citations:

Zbl 1092.06011
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References:

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