Sheffer Stroke Nelson Algebras

In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras and quotient sets on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. Also, it is shown that a s-Nelson algbera is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on s-Nelson algebra is determined by its ideal and quotient s-Nelson algebras are constructed by this congruence relation. Finally, it is indicated that a quotient s-Nelson algebra defined by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equals to 2.

Neutrosophic N-structures on Sheffer stroke BE-algebras

In this study, a neutrosophic N-subalgebra, a (implicative) neutrosophic N-filter, level sets of these neutrosophic N-structures and their properties are introduced on a Sheffer stroke BE-algebras (briefly, SBE-algebras). It is proved that the level set of neutrosophic N-subalgebras ((implicative) neutrosophic N-filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then it is proved that the family of all neutrosophic N-subalgebras of a SBE-algebra forms a complete distributive modular lattice. We present relationships between upper sets and neutrosophic N-filters of this algebra. Also, it is given that every neutrosophic N-filter of a SBE-algebra is its neutrosophic N-subalgebra but the inverse is generally not true. It is demonstrated that a neutrosophic N-structure on a SBE-algebra defi ned by a (implicative) neutrosophic N-filter of another SBE-algebra and a surjective SBE-homomorphism is a (implicative) neutrosophic N-filter. We present relationships between a neutrosophic N-filter and an implicative neutrosophic N-filter of a SBE-algebra in detail. Finally, certain subsets of a SBE-algebra are determined by means of N-functions and some properties are examined.

Conceptual Study and Manufacturing of a Configurable and Weld-Free Lattice Base for Automatic Food Machines

The study is aimed at developing a modular lattice base for automatic food machines, starting with a solution already patented by some of the authors. In this case, welded carpentry modules were interlocked with a system of profiles and metal inserts, also in welded carpentry, and the union was stabilized by structural adhesive bonding. Since welding involves long processing times and thermal distortions to be restored later, the driver of this study is to limit the use of welding as much as possible while increasing the modularity of the construction. For this purpose, various solution concepts have been generated where a common feature is the presence of rods of the same geometry and section to be joined together in configurable structural nodes. The concepts are qualitatively evaluated in light of the requirements, and the selected concept is digitally and physically prototyped. The prototype has been in service from over 5 years without showing any problems whatsoever.

Sectionally Pseudocomplemented Posets

The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension of relative pseudocomplementation for not necessarily distributive lattices. The typical example of such a lattice is the non-modular lattice N5. The aim of this paper is to extend the concept of sectional pseudocomplementation from lattices to posets. At first we show that the class of sectionally pseudocomplemented lattices forms a variety of lattices which can be described by two simple identities. This variety has nice congruence properties. We summarize properties of sectionally pseudocomplemented posets and show differences to relative pseudocomplementation. We prove that every sectionally pseudocomplemented poset is completely L-semidistributive. We introduce the concept of congruence on these posets and show when the quotient structure becomes a poset again. Finally, we study the Dedekind-MacNeille completion of sectionally pseudocomplemented posets. We show that contrary to the case of relatively pseudocomplemented posets, this completion need not be sectionally pseudocomplemented but we present the construction of a so-called generalized ordinal sum which enables us to construct the Dedekind-MacNeille completion provided the completions of the summands are known.

Smash product construction of modular lattice vertex algebras

<abstract><p>Motivated by a work of Li, we study nonlocal vertex algebras and their smash products over fields of positive characteristic. Through smash products, modular vertex algebras associated with positive definite even lattices are reconstructed. This gives a different construction of the modular vertex algebras obtained from integral forms introduced by Dong and Griess in lattice vertex operator algebras over a field of characteristic zero.</p></abstract>

On the notion of ranked complementedness in a lattice

Not every element in a lattice has a complement. In this paper we introduce a notion of ranked complement, which depends on a natural number [Formula: see text], so that for every element [Formula: see text] in a lattice with finite height there exists [Formula: see text] such that [Formula: see text] has a complement of rank [Formula: see text]. One of the main results we establish is that in a modular lattice having finite height, every element has a complement of rank less than [Formula: see text] if and only if there is a chain [Formula: see text] of elements such that each interval [Formula: see text] is a complemented lattice.

On the lattice of biorder ideals of regular rings

The study of biordered set plays a significant role in describing the structure of a regular semigroup and since the definition of regularity involves only the multiplication in the ring, it is natural that the study of semigroups plays a significant role in the study of regular rings. Here, we extend the biordered set approach to study the structure of the regular semigroup [Formula: see text] of a regular ring [Formula: see text] by studying the idempotents [Formula: see text] of the regular ring and show that the principal biorder ideals of the regular ring [Formula: see text] form a complemented modular lattice and certain properties of this lattice are studied.