Corpus ID: 237940667

New Results on Congruence Boolean Lifting Property

  title={New Results on Congruence Boolean Lifting Property},
  author={George Georgescu},
The Lifting Idempotent Property (LIP ) of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures (MV -algebras, commutative l-groups, BLalgebras, bounded distributive lattices, residuated lattices,etc.), as well as for some types of universal algebras (C. Muresan and the author defined and studied the Congruence Boolean Lifting Property (CBLP ) for congruence modular algebras). A lifting ideal of a ring R is an ideal of… Expand


Congruence Boolean Lifting Property
The main results of the present paper include a characterization theorem for congruence--distributive algebras with CBLP and a structure theorem for semilocal arithmetical algebraes with C BLP. Expand
The Reticulation of a Universal Algebra
A reticulation functor is defined and studied for the construction of the reticulations of any algebra A from a semi-degenerate congruence-modular variety C in the case when the commutator of A, applied to compact congruences of $A$, produces compact Congruences. Expand
Algebraic and topological results on lifting properties in residuated lattices
Topological characterizations are given to the lifting property for Boolean elements and several properties related to it, many of which are obtained by means of the reticulation. Expand
Lifting idempotents and exchange rings
Idempotents can be lifted modulo a one-sided ideal L of a ring R if, given x e R with x-x2 cL, there exists an idempotent e c R such that e x E L. Rings in which idempotents can be lifted moduloExpand
Central lifting property for orthomodular lattices
Abstract We introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that primeExpand
The spectrum problem for Abelian $$\ell $$-groups and MV-algebras
This paper deals with the problem of characterizing those topological spaces which are homeomorphic to the prime spectra of MV-algebras or Abelian l-groups. As a first main result, we show that aExpand
Generalizations of Boolean products for lattice-ordered algebras
  • P. Jipsen
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 2009
It is shown that FLw-algebras decompose as a poset product over any finite set of join irreducible strongly central elements, and that bounded n-potent GBL-alGEbras are represented as Esakia products of simple n- Potent MV-al gebras. Expand
Study of Pseudo BL – Algebras in View of Left Boolean Lifting Property
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Boolean Lifting Properties for Bounded Distributive Lattices
The lifting properties for the Boolean elements of bounded distributive lattices with respect to the congruences, filters and ideals are introduced and important classes of bounded distributed lattices are determined which satisfy these lifting properties. Expand
Further results on reticulated rings
For more details about the reticulation LR of a ring, see Simmons [9]. For any ideal I of the ring R, let D(I) be the ideal generated by {D(a) : a E I ) in LR. For any ideal J of the lattice LR, letExpand