Ring-like Structures Derived from Λ-lattices with Antitone Involutions

نویسنده

  • Ivan Chajda
چکیده

Using the concept of the λ-lattice introduced recently by V. Snášel we define λ-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On (finite) distributive lattices with antitone involutions

Some well-known algebras of logic or other algebraic models of non-classical reasoning, such as MV-algebras or orthomodular lattices, can be regarded as lattices with antitone involutions, i.e., bounded lattices with the property that all principal filters (or ideals) are equipped with antitone involutions. This simple observation is behind the so-called “basic algebras” that were introduced in...

متن کامل

Lattices and semilattices having an antitone involution in every upper interval

We study ∨-semilattices and lattices with the greatest element 1 where every interval [p,1] is a lattice with an antitone involution. We characterize these semilattices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilattices or lattices form varieties. The congruence prop...

متن کامل

Minimal Bounded Lattices with an Antitone Involution the Complemented Elements of Which Do Not Form a Sublattice

Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.

متن کامل

Completeness results for metrized rings and lattices

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

متن کامل

Polynomial permutations on bounded commutative directoids with an antitone involution

Main results of Dorninger and Länger (J Pure Appl Math 40:441–449, 2007) concerning polynomial permutations on bounded lattices with an antitone involution are generalized to the case of bounded commutative directoids.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007