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Jiří Rachunek 《Algebra Universalis》2002,48(2):151-169
Non-commutative generalizations of MV-algebras were introduced by G. Georgescu and A. Iorgulesco as well as by the author; the generalizations are equivalent and
are called GMV-algebras. We show that GMV-algebras can be considered as special cases of Grishin algebras. As MV-algebras are algebraic models of the Łukasiewicz logic and Grishin algebras have the analogous role for the classical bilinear
logic, GMV-algebras correspond to a non-commutative logic between the above logics. Further, by A. Dvurečenskij, any GMV-algebra is isomorphic to an interval of an l-group, which in general is not commutative. This generalizes D. Mundici's representation of MV-algebras by means of intervals of abelian l-groups. In the paper (using this representation) we describe the properties of prime ideal spectra of GMV-algebras and of their factor algebras and ideals and prove that the spectrum of closed ideals of any GMV-algebra is homeomorphic to that of a completely distributive GMV-algebra.
Received January 4, 2001; accepted in final form May 2, 2002. 相似文献
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Tong Daorong 《东北数学》1994,(2)
FreeWeaklyHamilitonianLattice-OrderedGroups¥TongDaorong(仝道荣)(DepartmentofMathematics,HehaiUniversity.Nanijng,210024)Abstract:... 相似文献
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Pierece证明了对于任意一个具有最小元0的分配格L,存在一个格态f:L→L满足:(1)Kerf=0;(2)f(a)=f(b)当且仅当a⊥=b⊥,这里a,b∈L,且对于x∈L,x⊥={y∈L:y∧x=0}。我们称这样的格同态为Pierece同态。本文我们将证明:如果G是一个Archimedeanl-群,则G+只有唯一的Pierece同态。 相似文献
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漆芝南 《南昌大学学报(理科版)》1990,14(3):1
本文得到以下主要结果:(1)G是l群,A,B∈P(G)\{(0)},且A∨B=G或A与B可比较,则A=A1’,其中A1是0-群.(2)G是l群,则Γ(G)满足DCC(ACC)当且仅当Γm(G)满足DCC(ACC)(3)l群G Bw,则G有基当且仅当∩△Gg=0。(4)若特殊值l群G∈D,则G有一小元素基 相似文献
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引入弱奇异元及弱奇异l-群的概念,通过建立弱奇异元及弱奇异l-群的刻划,研究了一般弱奇异l-群的性质及相关的结构,部分地改进了有关奇异l-群已有的结果. 相似文献
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