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1.
On L-fuzzy Ideals in Semirings I 总被引:1,自引:0,他引:1
In this paper we extend the concept of an L-fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring R, and we show that each level left (resp. right) ideal of an .L-fuzzy left (resp. right) ideal of R is characteristic iff is L-fuzzy characteristic. 相似文献
2.
Let be an algebra, and let X be an arbitrary -bimodule. A linear space Y ? X is called a Jordan -submodule if Ay + yA ∈ Y for all A ∈ and y ∈ Y. (For X = , this coincides with the notion of a Jordan ideal.) We study conditions under which Jordan submodules are subbimodules. General criteria are given in the purely algebraic situation as well as for the case of Banach bimodules over Banach algebras. We also consider symmetrically normed Jordan submodules over C*-algebras. It turns out that there exist C*-algebras in which not all Jordan ideals are ideals.
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3.
Zeng Guangxing 《中国科学A辑(英文版)》1999,42(3):272-280
For an ordered field (K,T) and an idealI of the polynomial ring
, the construction of the generalized real radical
ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing
is presented.
Project supported by the National Natural Science Foundation of China (Grant No. 19661002) and the Climbing Project. 相似文献
4.
In this paper, a characterization for an I(L)-topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I(L)-topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I(L)-topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I(L)-topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too. 相似文献
5.
Clemens Puppe 《Annals of Operations Research》1994,52(1):67-81
This paper studies vague preferences. In contrast to the concept of fuzzy preferences, the more general notion of vague preferences does not entail the assumption that the different degrees of preference are completely ordered. It is shown that the more general concept of a vague preference order arises very naturally in the context of aggregating a set of (exact) weak orders. Furthermore, necessary and sufficient conditions for the rationalizability of an exact choice function by means of a vague preference order are given. It turns out that in the general case these conditions are weaker than in the case where the degrees of preference are completely ordered. Consequently, there exist choice functions which are rationalizable by a general vague preference order but which are not rationalizable by a fuzzy preference order, or more generally by any vague preference order which induces a complete ranking of the degrees of preference. Examples of such choice functions are provided.This is a revised version of a discussion paper which was written at the University of Karlsruhe. I am grateful to Georg Bol and an anonymous referee for valuable comments. The research has been made possible by a fellowship of the DFG (Deutsche Forschungsgemeinschaft) which is also gratefully acknowledged. 相似文献
6.
An ideal I of a ring R is called normal if all idempotent elements in I lie in the center of R. We prove that if I is a normal ideal of an exchange ring R then: (1) R and R/I have the same stable range; (2) V(I) is an order-ideal of the monoid C(Specc(R), N), where Specc(R) consists of all prime ideals P such that R/P is local. 相似文献
7.
8.
In this note, we show by a counterexample that a proposition on L-homeomorphism property of the left and right translations in L-topological groups given by Bayoumi [On initial and final L-topological groups, Fuzzy Sets and Systems 156 (2005) 43–54] is incorrect, and offer its modified version. 相似文献
9.
We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence
kernels.
Work on the paper was supported by Council of Czech Government No J14/98:153100011. 相似文献
10.
Piotr Kalemba Szymon Plewik Anna Wojciechowska 《Central European Journal of Mathematics》2008,6(2):218-227
The σ-ideal (v
0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see
[9]. We introduce segment topologies to state some resemblances of (v
0) to the family of Ramsey null sets. To describe add(v
0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v
0) = add(v
0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v
0) = ω
1 implies that (v
0) has the ideal type (c, ω
1, c).
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11.
We present Gorenstein ideals of condimension 4 which have unimodal Hilbert functions.
The present studies were supported (in part) by the Basic Science Research Institute Program, BSRI 97-1423, Ministry of Education,
Korea 相似文献
12.
On fuzzy B-algebras 总被引:2,自引:0,他引:2
The fuzzification of (normal) B-subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy B-algebra is given. 相似文献
13.
Nobuaki Kuroki 《Fuzzy Sets and Systems》1981,5(2):203-215
In this paper we give some properties of fuzzy ideals and fuzzy bi-ideals of semigroups, and characterize semigroups that are (left) duo, (left) simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi-ideals. 相似文献
14.
Using the framework of ordered categories, the paper considers a generalization of the fuzzification machinery of algebraic structures introduced by Rosenfeld as well as provides a new approach to fuzzification of topological structures, which amounts to fuzzifying the underlying “set” of a structure in a suitably compatible way, leaving the structure itself crisp. The latter machinery allows the so-called “double fuzzification”, i.e., a fuzzification of something that is already fuzzified. 相似文献
15.
It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space L
p,w
(loc) does not hold in all this space and is satisfied only on some subspace. 相似文献
16.
The paper characterizes the length of maximal sequences satisfying conditions (i) and (ii) of (FC)-sequences, and proves some properties of (FC)-sequences, such as a bound on their lengths. As a consequence we get some results for mixed multiplicities and multiplicities of Rees rings of equimultiple ideals. We also prove that if is an ideal of positive height and is an arbitrary maximal sequence in satisfying conditions (i) and (ii) of (FC)-sequences, then is a reduction of
17.
It is shown that in a meet-continuous lattice L endowed with a multiplicative auxiliary order ≺ the family of all members of L which satisfy the axiom of approximation, i.e. α = {β ∈ L : β ≺ α}, is closed under finite infs and arbitrary sups. This is a key ingredient of a meet-continuous lattice proof that both regularity
and complete regularity of many valued topology have subbasic characterizations. As a consequence, the frame law can now be
eliminated from some fundamental results on completely regular L-valued topological spaces (e.g., this is the case in regard to the Tychonoff embedding theorem).
The grant MTM2006-14925-C02-02 from the Ministry of Education and Science of Spain and FEDER is gratefully acknowledged by
the second named author. 相似文献
18.
Andrzej Walendziak 《Mathematica Slovaca》2007,57(2):119-128
In this paper we introduce the notion of BF-algebras, which is a generalization of B-algebras. We also introduce the notions of an ideal and a normal ideal in BF-algebras. We investigate the properties and characterizations of them.
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19.
20.
G.X.-Z. Yuan 《Applied Mathematics Letters》1997,10(6):55-61
In this note, we first prove existence theorems for noncompact generalized quasivariational inequalities. As applications, two fixed point theorems for upper or lower semicontinuous multivalued mappings without compact domains are given in locally Hausdorff topological vector spaces. These results generalize or improve corresponding results in the literature. 相似文献