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Preface. List of Symbols. 1. Basic notions and results. 2. Compactly generated lattices. 3. Composition series. Decompositions. 4. Essential elements. Pseudo-complements. 5. Socle. Torsion lattices.… (More)
While any nil-clean ring is clean, the last eight years, it was not known whether nil-clean elements in a ring are clean. We give an example of nil-clean element in the matrix ring ℳ2(Z) which is not… (More)
As a special case of fully invariant subgroups, strongly invariant subgroups are introduced and studied for Abelian groups. 2010 Mathematics Subject Classification. 20K27, 20F99
The central idempotents of any ring with identity form a Boolean algebra. This result is largely extended for rings with generalized commuting idempotents.
A nonzero ring is said to be fine if every nonzero element in it is a sum of a unit and a nilpotent element. We show that fine rings form a proper class of simple rings, and they include properly the… (More)
Hypergroups associated with modular lattices, respectively compactly generated lattices, are studied and characterized.
In this note, steps in order to write a formula that gives the total number of subgroups of a finite abelian group are made.
Definition (Nachbin, Stenstrom) An element c of a complete lattice L is called compact if for every subset X of L and c ≤ ∨ X there is a finite subset F ⊆ X such that c ≤ ∨ F and S-compact if for… (More)
Definition. A system (A 1, A 2, ..., A n ; R) with A i 1 ≤ i ≤ n arbitrary sets and R ⊆ A 1 × A 2 × ... × A n is called an n-ary relation between the elements of these sets. If A 1 = A 2 = ... = A n… (More)