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1.
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
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纯正半群上的同余扩张(一) 总被引:1,自引:1,他引:0
刻划半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题.本文讨论了带上的同余的正规性和不变性以及在其Hall半群上的扩张,从同余扩张的角度刻划了带上的同余的性质,给出了扩张的极大、极小同余的描述. 相似文献
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Diego Vaggione 《Proceedings of the American Mathematical Society》1999,127(3):701-708
The notion of central idempotent elements in a ring can be easily generalized to the setting of any variety with the property that proper subalgebras are always nontrivial. We will prove that if such a variety is also congruence modular, then it has factorable congruences, i.e., it has the Fraser-Horn property. (This property is well known to have major implications for the structure theory of the algebras in the variety.)
5.
Ralph McKenzie 《Algebra Universalis》1991,28(4):589-603
We prove that in a locally finite variety with the congruence extension property, locally solvable congruences are central and locally solvable algebras are Hamiltonian. Also, we prove that a maximal subuniverse of a finite algebra in an Abelian variety is identical with an equivalence class of some congruence.Presented by H. P. Gumm. 相似文献
6.
This paper is a continuation of the earlier paper by the same authors in which a primary result was that every arithmetical affine complete variety of finite type is a principal arithmetical variety with respect to an appropriately chosen Pixley term. The paper begins by presenting an extension of this result to all finitely generated congruences and, as an example, constructs a closed form solution formula for any finitely presented system of pairwise compatible congruences (the Chinese remainder theorem). It is also shown that in all such varieties the meet of principal congruences is also principal, and finally, if a minimal generating algebra of the variety is regular, it is shown that the variety is also regular and the join of principal congruences is again principal. 相似文献
7.
As a sequel to [23] we investigate ideal properties focusing on subtractive varieties. After having listed a few basic results, we give several characterizations of the commutator of ideals and prove, for example, that it commutes with finite direct products. We deal with the ideal extension property (IEP) and with related commutator properties, showing for instance that IEP implies that the commutator commutes with restriction to subalgebras. Then we characterize varieties with distributive ideal lattices and relate this property with (a form of) equationally definable principal ideals and with IEP. Then, at the other extreme, we deal with Abelian and Hamiltonian properties (of ideals and congruences), giving for example a purely ideal theoretic characterization of varieties of Abelian groups with linear operations. To finish with, we present a few examples aiming at vindicating our work.Presented by A. F. Pixley. 相似文献
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Hanamantagouda P. Sankappanavar 《Algebra Universalis》1990,27(2):248-253
A formula is given to express a principal congruence on a double demi-p-lattice as a join of countably many principal lattice congruences. It is then applied to show that the variety of double demi-p-lattices has the congruence extension property. As special cases one obtains some known results for distributive doublep-lattices due to T. Hecht and T. Katriák.Presented by Bjarni Jónsson. 相似文献
10.
Mojgan Mahmoudi Halimeh Moghbeli Konrad Pióro 《Journal of Pure and Applied Algebra》2019,223(10):4161-4170
The study of algebraic properties of ordered structures has shown that their behavior in many cases is different from algebraic structures. For example, the analogues of the fundamental mapping theorem for sets which characterizes surjective maps as quotient sets modulo their kernel relations, is not true for order-preserving maps between posets (partially ordered sets). The main objective of this paper is to study the quotients of dcpos (directed complete partially ordered sets), and their relations with surjective dcpo maps (directed join preserving maps). The motivation of studying such infinitary ordered structures is their importance in domain theory, a theory on the borderline of mathematics and theoretical computer science.In this paper, introducing the notion of a pre-congruence on dcpos (directed complete partially ordered sets), we give a characterization of dcpo congruences. Also, it is proved that unlike natural dcpo congruences, the dcpo congruences are precisely kernels of surjective dcpo maps. Also, while it is known that the image of a dcpo map is not necessarily a subdcpo of its codomain, we find equivalent conditions on a dcpo map to satisfy this property. Moreover, we prove the Decomposition Theorem and its consequences for dcpo maps. 相似文献
11.
Congruence Permutable Symmetric Extended de Morgan Algebras 总被引:1,自引:0,他引:1
Jie FANG 《数学学报(英文版)》2006,22(3):659-664
An algebra A is said to be congruence permutable if any two congruences on it are permutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,0-algebras. In this paper, we study the class of symmetric extended de Morgan algebras that are congruence permutable. In particular we consider the case where A is finite, and show that A is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras. 相似文献
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Hernando Gaitán 《Czechoslovak Mathematical Journal》2003,53(3):631-639
In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety. 相似文献
13.
刻画半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题(参见[1-5])本文在[6]讨论了带上的同余的正规性和不变性以及在其Hall半群上的扩张的基础上,从同余扩张的角度刻划了完全正则的纯正半群的特征(定理26),给出了一个纯正半群的带上的所有同余都可以扩张到这个纯正半群的充分必要条件. 相似文献
14.
A. Ursini 《Algebra Universalis》2000,43(1):51-78
In a congruence modular subtractive variety there are both the commutator of ideals and the commutator of congruences. We prove that, if I' is the smallest congruence having an ideal I as a congruence class, then [I,J] = 0 /[I', J']. The general identity [0/ !,0 / #] = 0/[!,#] for !, # congruences, does not always hold; we give several conditions equivalent to this identity and sufficient conditions for it to hold. In the meantime, we get some other characterizations of the commutator of ideals. We also deal with the equational definability of principal commutators in a subtractive variety and with the extension property of the commutator from ideals of a subalgebra to the commutator of ideals of the whole algebra. 相似文献
15.
本文研究了伪补MS-代数的同余关系.利用正则滤子和伪补代数的对偶窄间理论,得到了正则滤子所生成的同余关系的性质以及同余可换的伪补MS-代数类,从而推广了文献[9]的结果. 相似文献
16.
Andrzej Walendziak 《Czechoslovak Mathematical Journal》2002,52(1):117-127
Here we consider the weak congruence lattice
of an algebra
with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices. 相似文献
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It is well known that the smallest semilattice congruence can be described via filters. We generalise this result to the smallest
left (right) normal band congruences and also to arbitrary semilattice (left normal band, right normal band) congruences,
describing them all via filters. To achieve this, we introduce filters relative to arbitrary quasiorders on a semigroup (traditional
filters are filters relative to the smallest negative operation-compatible quasiorder). We study congruences which can be
described via filters. We show that the lattice of semilattice (left normal band, right normal band) congruences is a homomorphic
image of the lattice of negative (right negative, left negative) operation-compatible quasiorders. 相似文献
19.
Hanamantagouda P. Sankappanavar Júlia Vaz de Carvalho 《Mathematical Logic Quarterly》2014,60(6):425-436
In this paper we first describe the Priestley duality for pseudocomplemented De Morgan algebras by combining the known dualities of distributive p‐algebras due to Priestley and for De Morgan algebras due to Cornish and Fowler. We then use it to characterize congruence‐permutability, principal join property, and the property of having only principal congruences for pseudocomplemented De Morgan algebras. The congruence‐uniform pseudocomplemented De Morgan algebras are also described. 相似文献
20.
Brunetto Piochi 《Algebra Colloquium》2000,7(1):59-72
We study the lattice. C(S) of congruences of a monoid S which is the Bruck-Reilly extension of a monoid T by a homomorphism . The inclusion, meet and join of congruences are described in terms of congruences and ideals of T. We show that C(S) can be naturally decomposed into three sublattices, corresponding (roughly speaking) to the three different types of congruences on such semigroups.1991 Mathematics Subject Classification: 20M10 相似文献