Existence of Endo-rigid Boolean Algebras
نویسنده
چکیده
How many endomorphisms does a Boolean algebra have? Can we find Boolean algebras with as few endomorphisms as possible? Of course from any ultrafilter of the Boolean algebra we can define an endomorphism, and we can combine finitely many such endomorphisms in some reasonable ways. We prove that in any cardinality λ = λ0 there is a Boolean algebra with no other endomorphisms. For this we use the so called “black boxes”, but in a self contained way. We comment on how necessary the restriction on the cardinal is.
منابع مشابه
Filter theory in MTL-algebras based on Uni-soft property
The notion of (Boolean) uni-soft filters in MTL-algebras is introduced, and several properties of them are investigated. Characterizations of (Boolean) uni-soft filters are discussed, and some (necessary and sufficient) conditions for a uni-soft filter to be Boolean are provided. The condensational property for a Boolean uni-soft filter is established.
متن کاملOn some classes of expansions of ideals in $MV$-algebras
In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate and $ (tau,sigma)$-Boolean in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...
متن کاملSpectra of Tukey Types of Ultrafilters on Boolean Algebras
Extending recent investigations on the structure of Tukey types of ultrafilters on P(ω) to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras. These include the classes of free Boolean algebras, superatomic Boolean algebras generated by almost disjoint families, interval algebras, tree algebras, and pseudo-tree algebras. W...
متن کاملOmega-almost Boolean rings
In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.
متن کاملDually quasi-De Morgan Stone semi-Heyting algebras II. Regularity
This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011