residual of ideals of an l-ring
Authors
abstract
the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of an ideal of ordinary rings are extended to l-ideal theory ofl-subrings.
similar resources
RESIDUAL OF IDEALS OF AN L-RING
The concept of right (left) quotient (or residual) of an ideal η by anideal ν of an L-subring μ of a ring R is introduced. The right (left) quotients areshown to be ideals of μ . It is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an L-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . Most of the results pertaining to the notion of quotients(or residual) of ...
full textON FUZZY IDEALS OF A RING
The concepts of L-fuzzy ideal generated by a L-fuzzy subset, L-fuzzy prime and completely prime ideal where L is a complete lattice are considered and some results are proved
full textEMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO ITS LATTICE OF FUZZY IDEALS
We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , sin [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...
full textHomomorphism IN (Q, L) -Fuzzy Normal Ideals of a Ring
In this paper, we study some of the properties of (Q, L) -fuzzy normal ideal of a ring and prove some results on these. 2000 AMS SUBJECT CLASSIFICATION: 03F55, 08A72, 20N25.
full textRing Ideals
We introduce the basic notions of ideal theory in rings. This includes left and right ideals, (finitely) generated ideals and some operations on ideals such as the addition of ideals and the radical of an ideal. In addition we introduce linear combinations to formalize the well-known characterization of generated ideals. Principal ideal domains and Noetherian rings are defined. The latter devel...
full textResidual Ideals of Maclane Valuations
Let K be a field equipped with a discrete valuation v. In a pioneering work, MacLane determined all valuations on K(x) extending v. His work was recently reviewed and generalized by Vaquié, by using the graded algebra of a valuation. We extend Vaquié’s approach by studying residual ideals of the graded algebra as an abstract counterpart of certain residual polynomials which play a key role in t...
full textMy Resources
Save resource for easier access later
Journal title:
iranian journal of fuzzy systemsPublisher: university of sistan and baluchestan
ISSN 1735-0654
volume 4
issue 2 2007
Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023