Ke Yun Qin, Yang Xu, Young Bae Jun (2002)
Czechoslovak Mathematical Journal
Similarity:
We define an ultra -ideal of a lattice implication algebra and give equivalent conditions for an -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra -ideal.
Ivan Chajda, Jiří Rachůnek (2001)
Czechoslovak Mathematical Journal
Similarity:
The concepts of an annihilator and a relative annihilator in an autometrized -algebra are introduced. It is shown that every relative annihilator in a normal autometrized -algebra is an ideal of and every principal ideal of is an annihilator of . The set of all annihilators of forms a complete lattice. The concept of an -polar is introduced for every ideal of . The set of all -polars is a complete lattice which becomes a two-element chain provided is prime. The -polars...
Y. S. Pawar, S. S. Khopade (2010)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Similarity:
In a 0-distributive lattice sufficient conditions for an -ideal to be an annihilator ideal and prime ideal to be an -ideal are given. Also it is proved that the images and the inverse images of -ideals are -ideals under annihilator preserving homomorphisms.
Yu Xi Zou, Xiao Long Xin, Peng Fei He (2016)
Open Mathematics
Similarity:
In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,0, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study...