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We characterize clean elements of $ℛ (L)$ and show that $α \in ℛ (L)$ is clean if and only if there exists a clopen sublocale $U$ in $L$ such that $𝔠_{L} (coz (α - 1)) \subseteq U \subseteq 𝔬_{L} (coz (α))$ . Also, we prove that $ℛ (L)$ is clean if and only if $ℛ (L)$ has a clean prime ideal. Then, according to the results about $ℛ (L),$ we immediately get results about $𝒞_{c} (L) .$

The coherent algebras in the varieties $K_{n, m}$ of Ockham algebras

Ramalho, Margarita (1993)

Portugaliae mathematica

The completely distributive lattice of machine invariant sets of infinite words

Aleksandrs Belovs, Jānis Buls (2007)

Discussiones Mathematicae - General Algebra and Applications

We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.

The distributivity property of valuation rings

Ján Mináč (1981)

Mathematica Slovaca

The double powerlocale and exponentiation: A case study in geometric logic.

Vickers, Steven (2004)

Theory and Applications of Categories [electronic only]

The dual of the category of generalized trees.

Basarab, Şerban (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

The essential cover and the absolute cover of a schematic space

Wolfgang Rump, Yi Chuan Yang (2009)

Colloquium Mathematicae

A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component,...

The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks

Zdena Riečanová (2008)

Kybernetika

Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which...

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$T_{2}$ -frames and almost compact frames

$T_{2}$ -separation axioms on frames

$T$ -algebras of the monad $L$ -Fuzz

$T o p^{o p}$ is a quasi-variety

Tensor products of semilattices and distributive lattices.

The 0-distributivity in the class of subalgebra lattices of Heyting algebras and closure algebras

The algebra of first-order fuzzy logic

The Chinese remainder theorem and sheaf representations

The clean elements of the ring $ℛ (L)$

The coherent algebras in the varieties $K_{n, m}$ of Ockham algebras

The completely distributive lattice of machine invariant sets of infinite words

The distributivity property of valuation rings

The double powerlocale and exponentiation: A case study in geometric logic.

The dual of the category of generalized trees.

The essential cover and the absolute cover of a schematic space

The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks

The exocenter of a double Heyting algebra

The frame of fibrewise closed nuclei

The ideal structure of simple ternary algebras

The lattice of bi-numerations of arithmetic. I.

Currently displaying 1 – 20 of 51