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Y. S. Pawar, S. S. Khopade (2010)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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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.
M. Sambasiva Rao (2012)
Archivum Mathematicum
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The concept of -ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of -ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of -ideals. Finally, some properties of -ideals are studied with respect to homomorphisms and filter congruences.
Marshall Harvey Stone (1938)
Časopis pro pěstování matematiky a fysiky
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Marcel Erné (2006)
Mathematica Slovaca
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Yu Xi Zou, Xiao Long Xin, Peng Fei He (2016)
Open Mathematics
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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...