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Papers by Abu Saleh Abdun Noor

Commentationes Mathematicae Universitatis …, 1987

... 2, 199--210 Persistent URL: http://dml.cz/dmlcz/106531 Terms of use: © Charles University in ... more ... 2, 199--210 Persistent URL: http://dml.cz/dmlcz/106531 Terms of use: © Charles University in Prague, Faculty of Mathematics and Physics, 1987 ... Again, anbsaAb^ ) . So (anb)Aj(a,b,'c) & aAbAj(a ,b,c) = = aAbO ), and hence (anb)Aj(a ,b,c) = (aAb)v((anb)Aj(a ,b,c)An). ...

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE 27,4 (1986) MULTIPLIERS ON A NEAR LATTICE A. S. A. NOOR and William H. CORNISH Abstrаct A nearlattice is a lower semilattice in which any two elements have a supremum whenever they are bounded above. Here we generalize the con cept of direct summand to nearlattices and show that the direct summands of a nearlattice S with 0 are precisely the central elements of J(S), the lattice of ideals. Then we discuss multipliers (meet translations) on nearlattices.

Nearlattices, or lower semilattices in which any two elements have a supremum whenever they are b... more Nearlattices, or lower semilattices in which any two elements have a supremum whenever they are bounded above, provide an interesting generalization of lattices. In this context, we define different types of elements in a nearlattice S and then for a fixed element n, using the ternary operation J , study the behaviour of S =(S;n) where x r.y = (x A y ) \'(x A n) v v (y A n); x , y 6 S . Key words-; Standard element, neutral element, n e a r l a t t i c e . Classification: 06A12, 06A99, 06B10 1 . Introduction. A nearlattice is a lower semilattice which has the property that any two elements possessing a common upper bound, have a supremum. Cornish and Hickman 111 called this the upper bound p r o p e r t y . For detailed literature, we refer the reader to consult [13,12] and [ 7V A nearlattice-congruence $ on a nearlattice S is a congruence of the underlying lower semilattice such that, whenever a,5Eb,, a 2-=b 2($) and a,va 2, b, vb„ exist, a, v a2 s b, v b«( <£ ) . In the sec...

Mathematica Bohemica

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Commentationes Mathematicae Universitatis Carolinae, 1986

Bulletin of the Australian Mathematical Society, 1980

This thesis studies the nature of isotopes of a nearlattice. A nearlattice is a lower semilattice... more This thesis studies the nature of isotopes of a nearlattice. A nearlattice is a lower semilattice with the upper bcund property, which says that any two elements possess a supremum whenever they have a common upper bound. The topic arose out of a study on the kernels, around a particular element n , of a skeletal congruence on a distributive lattice. Also, we found that the idea of an isotope was very fruitful in extending results on ideals of nearlattices to the w-ideals; that is, convex subnearlattices containing n. Chapter 1 discusses ideals, join-partial congruences and other results on nearlattices which are basic to this thesis. Chapters 2 and 3 introduce

Bulletin of the Australian Mathematical Society, 1982

Nearlattices, or lower semllattices in which any two elements have a supremum whenever they are b... more Nearlattices, or lower semllattices in which any two elements have a supremum whenever they are bounded above, provide an interesting generalization of lattices. In this context, we study standard, neutral, and central elements, as well as standard ideals. A new perspective is obtained in the well established case of lattices.