Ladislav Beran (1998)
Commentationes Mathematicae Universitatis Carolinae
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This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.
Ladislav Beran (1994)
Commentationes Mathematicae Universitatis Carolinae
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The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. -radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of -radicals. In addition, a necessary and sufficient condition...
Shriram K. Nimbhorkar, Rupal C. Shroff (2015)
Czechoslovak Mathematical Journal
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The concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced. In a modular lattice satisfying a certain condition, a characterization is given for direct summands of an extending ideal to be mutually ojective. We define exchangeable decomposition and internal exchange property of an ideal in a modular lattice....
Ladislav Beran (1995)
Collectanea Mathematica
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João Pita Costa (2012)
Discussiones Mathematicae - General Algebra and Applications
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Ideals are one of the main topics of interest when it comes to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be derived, respectively, from the two concepts of order that arise in the context of skew lattices. The correspondence between the ideals of a skew lattice, derived from the preorder, and the ideals of its respective lattice image is clear....