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1.
Zhu Linsheng 《东北数学》1998,(1)
in this paper, the classification and realization of complete Lie algebras withcommutative nilpotent radicals are given. From this, some results on the radicals of thesecomplete Lie algebras are obtained. 相似文献
2.
Eleftherios Gkioulekas 《International Journal of Mathematical Education in Science & Technology》2018,49(8):1278-1292
The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original equation. We propose alternative solution procedures that are rigorous and simple to execute where the extraneous solutions can be identified without verification against the original equation. In this article, we review previous literature, establish and illustrate rigorous solution procedures for radical equations of depth 1 (i.e. equations where all radicals can be eliminated in one step), and deal with an ambiguity concerning the definition of real-valued solutions to radical equations. An application to defining the inverse function, resulting in a parametric radical equation, is also explained. 相似文献
3.
Fuzzy半群中的Fuzzy素理想 总被引:4,自引:2,他引:2
探讨Fuzzy半群中Fuzzy素理想,Fuzzy 完全理想与Fuzzy理想的根的一些代数性质,证明Fuzzy半群中每一个Fuzzy理想是Fuzzy完全半素理想当且仅当它可表为一族Fuzzy完全素理想之交。 相似文献
4.
A fuzzy rule-based system for handwritten Chinese characters recognition based on radical extraction 总被引:1,自引:0,他引:1
In this paper, a fuzzy rule-based system for handwritten Chinese characters recognition (HCCR) based on radical extraction is proposed. Since the writings of handwritten Chinese characters vary a lot, we adopt fuzzy set theory to deal with the recognition of these fuzzy patterns. Candidates of strokes are provided with confidence values to obtain more reliable and accurate results. Furthermore, hierarchical fuzzy rule sets that represent the character structures are used to combine the extracted strokes into compound strokes or radicals. The flexible expansion ability thus provided is very promising. Also, since the number of rules in a fuzzy system is much less than that in a general rule-based system, the computation effort is not difficult. An average of 99.63% recognition rate of 542 test categories that are selected from the 100th sample set of HCCRBASE (character image database provided by CCL, ITRI, Taiwan) is obtained. The experimental results not only verify the feasibility of the proposed system, but also suggest that applying fuzzy set theory to HCCR is an efficient and promising approach. 相似文献
5.
6.
In this note we prove that the prime madicals of some graded rings and the scoles of some graded modules are also graded. The results on the relations between the prime radical and the graded prime radical are also presented. Moreover, the relations between a graded ring and its initial subring are studied. 相似文献
7.
A lattice-theoretic approach to the radical theory of rings was initiated by Snider. In the current paper, we extend this approach to the radical theory of involution rings. We show that the classes of hereditary radicals, radicals satisfying ADS and invariant radicals form complete sublattices of the lattice of all radicals of involution rings. We show that certain sublattices are isomorphic to sublattices of the lattice of radicals of rings. We characterize the atoms of certain lattices of radicals of involution rings.1991 Mathematics Subject Classification: 16W10, 16N99, 06B99 相似文献
8.
结合环根论中由具有单位元的单环类所确定的上根就是Brown-McCoy根.本文指出在Γ-环中,鉴于Γ-环单位元的复杂性质使得有幺单Γ-环类确定的上根演变成8个,进而研究了这些根之间及这些根与Γ-环其它根之间的大小关系. 相似文献
9.
Summary We continue our study of the lattice of matric-extensible radicals of associative rings. We find some atoms generated by
simple rings of the lattices of all matric-extensible radicals, matric-extensible supernilpotent radicals and matric-extensible
special radicals. We consider *-rings, which were previously defined by the second author, and consider when they generate
atoms of these lattices. 相似文献
10.
11.
《代数通讯》2013,41(6):2883-2896
Abstract In 1945, N. Jacobson has introduced the definition of radical of a ring A (which is known as “Jacobson radical”, and is denoted J = J(A)). Later the concept of (Jacobson) radical of a left (or right) A-module M, J(M), has been defined as the intersection of all submodules N ≤ M such that M/N is simple. Thus one may consider the left radical J l = J( A A) and the right radical J r = J(A A ) of A, which are bilateral ideals of A, and are contained in J(A). If A has identity, one has J = J l = J r , but this equality is not valid in general. Dual, it is possible to define left socle S l and right socle S r of A. We shall establish relations between J, J l , J r , S l and S r , and for artinian algebras we shall obtain expressions for J l (A) and J r (A), S l (A) and S r (A). In particular, if A is a finite dimensional algebra over a field we display J l = J( A A) (and J r ? J(A A )) in a matrix representation. 相似文献
12.
代数正规类中的遗传根与强半单根 总被引:5,自引:0,他引:5
Puczylowski建立了一般代数对象类的根理论.本文在代数正规类中,用格论方法刻划一般遗传根和强半单根类,探究它们的一些性质,推广了已知各类代数系统的某些根论研究. 相似文献
13.
0.IntroductionInthispaper,HalwaysdenoteaHopfalgebraoverafieldK,andwefolowthenota-tionsinSweedle’sbook[1].ForgeneraltheoryofH-... 相似文献
14.
A. V. Kelarev 《Semigroup Forum》1991,43(1):291-298
It is well-known that semigroups of many important classes are decomposable into bands of their subsemigroups with more “rigid”
structure. For efficient applications of radicals to semigroups of that kind, an information on the shape of radicals in bands
of semigroups may be useful. Here we will investigate the Jacobson, Baer, Brown-McCoy and the least special radicals. The
results were announced in [3]. The interaction of bands and radicals was also considered in [4] for the class of semigroups
with zero; analogous problems for bands and radicals of associative rings were investigated in [5], [6] and [7]. 相似文献
15.
16.
分次根、弱分次根与自反根 总被引:12,自引:0,他引:12
本文在一般群分次环范畴中,给出了典型分次根NG,LG,gG,rG和KG的元素刻划.通过建立弱分次根概念,研究了自反根Nref,Lref,gref,rref和Kref的性质,探讨了这些分次根和与它们相对应的自反根的关系. 相似文献
17.
TheJacobsonandBrown-McCoyRadicalsofCertain Group RingsZhouYongxin(周永新)(Math.Dept.,HebeiTeachers'University,Shijiazhuang,05001... 相似文献
18.
S. Tumurbat 《Acta Mathematica Hungarica》2001,93(1-2):99-108
Principally left strong radicals were introduced in [4]. Here, we continue to study such radicals. Principally left strong
radicals and their semisimple classes are characterized in Section 2. Sections 3 and 4 are devoted to the lower principally
left strong radical construction and to the upper principally left strong radical construction, respectively.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
19.
关于绝对半素环和绝对半素根 总被引:3,自引:0,他引:3
张宪君 《纯粹数学与应用数学》1993,9(2):57-60
本文了绝对半素环的概念,研究了绝对半素与与半素环及素环之间的关系,讨论了由全体绝对半素环类决定的上根--绝对半半素根及其性质。 相似文献
20.
E. A. Timoshenko 《Journal of Mathematical Sciences》2008,154(3):411-421
This paper is devoted to the class of idempotent radicals defined by means of a tensor product. We describe their effect on
Abelian groups. The structure of the lattice of all such radicals is determined. We characterize these radicals in terms of
the closure properties of their radical classes.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 3, pp. 193–208, 2007. 相似文献