共查询到19条相似文献,搜索用时 109 毫秒
1.
对偶根和F.A.SZSZ问题21 总被引:1,自引:0,他引:1
本文证明了根 R 的补根是由所有非 R-半单的亚直既约环确定的上根.对半遗传根,给出了补根的进一步刻划,证明了遗传根是对偶根,当且仅当它是由一个亚直既约环环类确定的上根,每个遗传对偶根或者是超幂零的,或者是次幂等的. 相似文献
2.
本文证明了根 R 的补根是由所有非 R-半单的亚直既约环确定的上根.对半遗传根,给出了补根的进一步刻划,证明了遗传根是对偶根,当且仅当它是由一个亚直既约环环类确定的上根,每个遗传对偶根或者是超幂零的,或者是次幂等的. 相似文献
3.
F.A.Szasz在[1]中提出公开问题55:设K是Jacobson根为零的全体亚直既约环类,研究类K确定的上根.本文对此进行了研究,证明了Jacobson根为零的全体亚直既约环类K确定的上根R是特殊根,它介于Jacobson根与Brown-McCoy根之间.并给出任意结合环A为R-根环的充要条件. 相似文献
4.
σ-根与σ-半单类的构造 总被引:1,自引:0,他引:1
继[1~3]分别给出σ-根及其半单类的两个特征性质,研究了对于已知环类M,含于M的最大σ-根及σ-半单类和包含M的最小σ-半单类的构造,同时得到σ-半单闭包σ-遗传的一个充分条件. 相似文献
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设M是任意环类,u,ψ分别表示上根算子及半单算子。W.G.Leavitt在[1]中研究了uM成为遗传根的充要条件。本文将讨论ψM成为半单类,本质闭类,同态闭类或具有其它环类性质的一些等价条件。作为推论,最后给 相似文献
7.
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
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10.
厉立德 《数学年刊A辑(中文版)》1982,(6)
Bourno与Zassenhaus, Lizuka分别定义了半环的Jacobson根。但是刻划关于这种根的半单类的最好结果是LaTorre所证明的,Jacobson根为零的半环“半同构”于本原半环的亚直和。本文将以定义在半环上的几类特殊的等价关系为基础,来探讨任 相似文献
11.
Ralph McKenzie 《Algebra Universalis》1983,17(1):143-149
It is proved for any varietyG of groups that if the subdirectly irreducible groups inG form a set, and if the subdirectly irreducible representation algebras of groups inG form a set, then every finite group inG is Abelian. The result is essential for the characterization of residually finite varieties of semigroups. 相似文献
12.
讨论了分次环A,Ae和A#G*的相关性质,在A是分次忠实时,A#G*是亚直既约环当且仅当Ae是亚直既约环;在A是分次非退化时,A#G*是G亚直既约环当且仅当A是分次亚直既约环. 相似文献
13.
Commutative multiplicatively idempotent semirings were studied by the authors and F. ?vr?ek, where the connections to distributive lattices and unitary Boolean rings were established. The variety of these semirings has nice algebraic properties and hence there arose the question to describe this variety, possibly by its subdirectly irreducible members. For the subvariety of so-called Boolean semirings, the subdirectly irreducible members were described by F. Guzmán. He showed that there were just two subdirectly irreducible members, which are the 2-element distributive lattice and the 2-element Boolean ring. We are going to show that although commutative multiplicatively idempotent semirings are at first glance a slight modification of Boolean semirings, for each cardinal n > 1, there exist at least two subdirectly irreducible members of cardinality n and at least 2n such members if n is infinite. For \({n \in \{2, 3, 4\}}\) the number of subdirectly irreducible members of cardinality n is exactly 2. 相似文献
14.
Yu. M. Movsisyan V. A. Aslanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(6):241-246
The paper characterizes the class of subdirectly irreducible algebras satisfying hyperidentities of the variety of De Morgan algebras. Such algebras are called subdirectly irreducible De Morgan quasilattices. The suggested characterization is quite close to that of the classical case of subdirectly irreducible DeMorgan algebras. 相似文献
15.
Anvar M. Nurakunov 《Algebra Universalis》2017,78(2):181-192
An algebraic structure A is said to be finitely subdirectly reducible if A is not finitely subdirectly irreducible. We show that for any signature providing only finitely many relation symbols, the class of finitely subdirectly reducible algebraic structures is closed with respect to the formation of ultraproducts. We provide some corollaries and examples for axiomatizable classes that are closed with respect to the formation of finite subdirect products, in particular, for varieties and quasivarieties. 相似文献
16.
J. A. Gerhard 《Semigroup Forum》1972,5(1):362-369
Subdirectly irreducible idempotent semigroups were characterized in [3], and in that paper, their connection with the various
equational classes of idempotent semigroups was discussed. All these results are in terms of identities, so that examples
of subdirectly irreducibles in the equational classes are explicitly known only for small classes. It is easy to show from
general considerations (see the last section of the present paper) that every proper equational subclass of the class of idempotent
semigroups is generated (as an equational class) by one or two subdirectly irreducibles. In this paper we give an example
of a subdirectly irreducible for each join irreducible equational class of idempotent semigroups, which generates the class.
This list, together with known results, gives explicit examples of one or two finite subdirectly irreducibles which generate
the various equational classes.
Research supported by the National Research Council of Canada. 相似文献
17.
Ján Jakubík 《Mathematica Slovaca》2010,60(2):179-188
The notion of idempotent modification of an algebra was introduced by Je?ek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved. 相似文献
18.
Generalizing the well known and exploited relation between Heyting and Nelson algebras to semi-Heyting algebras, we introduce the variety of semi-Nelson algebras. The main tool for its study is the construction given by Vakarelov. Using it, we characterize the lattice of congruences of a semi-Nelson algebra through some of its deductive systems, use this to find the subdirectly irreducible algebras, prove that the variety is arithmetical, has equationally definable principal congruences, has the congruence extension property and describe the semisimple subvarieties. 相似文献
19.
考察了扩张的有界分配格类eD即带有自同态k的有界分配格,研究了具有幂等性的eD-代数的表示、同余关系以及次直不可约性,证明了这样的代数类有5个互不同构的次直不可约的幂等扩张的有界分配格。 相似文献