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Weakly 2‐Absorbing Ideals in Almost Distributive Lattices
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The concepts of weakly 2‐absorbing ideal and weakly 1‐absorbing prime ideal in an almost distributive lattice (ADL) are introduced, and the necessary conditions for a weakly 1‐absorbing prime ideal to become a weakly 2‐absorbing ideal in algebraic form are proved. Also, weakly 2‐absorbing ideals are characterized in terms of weakly prime ideals and 2‐absorbing ideals. Finally, the lattice epimorphic images and inverse images of the weakly 2‐absorbing ideal and weakly 1‐absorbing prime ideal are discussed.
Title: Weakly 2‐Absorbing Ideals in Almost Distributive Lattices
Description:
The concepts of weakly 2‐absorbing ideal and weakly 1‐absorbing prime ideal in an almost distributive lattice (ADL) are introduced, and the necessary conditions for a weakly 1‐absorbing prime ideal to become a weakly 2‐absorbing ideal in algebraic form are proved.
Also, weakly 2‐absorbing ideals are characterized in terms of weakly prime ideals and 2‐absorbing ideals.
Finally, the lattice epimorphic images and inverse images of the weakly 2‐absorbing ideal and weakly 1‐absorbing prime ideal are discussed.
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