scholarly journals Sheffer Stroke Nelson Algebras

2021 ◽  
Author(s):  
Tahsin Oner ◽  
Tugce Katican ◽  
Arsham Borumand Saeid
Keyword(s):  
Modular Lattice ◽  
Congruence Relation ◽  
Algebraic Structures ◽  
Sheffer Stroke ◽  
Nelson Algebra ◽  
The Family ◽  
Nelson Algebras

Abstract 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.

scholarly journals Neutrosophic N-structures on Sheffer stroke BE-algebras

2021 ◽  
Author(s):  
Tahsin Oner ◽  
Tugce Katican ◽  
Salviya Svanidze ◽  
Akbar Rezaei
Keyword(s):  
Level Set ◽  
Modular Lattice ◽  
Level Sets ◽  
Sheffer Stroke ◽  
The Family

Abstract 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.

scholarly journals Soft Set Theory Applied to Hoops

2020 ◽  
Vol 28 (1) ◽  
pp. 61-79
Author(s):  
R. A. Borzooei ◽  
E. Babaei ◽  
Y. B. Jun ◽  
M. Aaly Kologani ◽  
M. Mohseni Takallo
Keyword(s):  
Set Theory ◽  
Congruence Relation ◽  
Heyting Algebra ◽  
Soft Set ◽  
The Family ◽  
Different Types

AbstractIn this paper, we introduced the concept of a soft hoop and we investigated some of their properties. Then, we established different types of intersections and unions of the family of soft hoops. We defined two operations ⊙ and → on the set of all soft hoops and we proved that with these operations, it is a hoop and also is a Heyting algebra. Finally we introduced a congruence relation on the set of all soft hoops and we investigated the quotient of it.

scholarly journals Filters of strong Sheffer stroke non-associative MV-algebras

2021 ◽  
Vol 29 (1) ◽  
pp. 143-164
Author(s):  
Tahsin Oner ◽  
Tugce Katican ◽  
Arsham Borumand Saeid ◽  
Mehmet Terziler
Keyword(s):  
Congruence Relation ◽  
Sheffer Stroke ◽  
Isomorphism Theorems ◽  
Mv Algebras

Abstract In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

scholarly journals Constructing Some Logical Algebras with Hoops

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1243
Author(s):  
M. Aaly Kologani ◽  
Seok-Zun Song ◽  
R. A. Borzooei ◽  
Young Bae Jun
Keyword(s):  
Congruence Relation ◽  
Heyting Algebras ◽  
Algebraic Structures ◽  
Hilbert Algebras ◽  
Wajsberg Hoops

In any logical algebraic structures, by using of different kinds of filters, one can construct various kinds of other logical algebraic structures. With this inspirations, in this paper by considering a hoop algebra or a hoop, that is introduced by Bosbach, the notion of co-filter on hoops is introduced and related properties are investigated. Then by using of co-filter, a congruence relation on hoops is defined, and the associated quotient structure is studied. Thus Brouwerian semilattices, Heyting algebras, Wajsberg hoops, Hilbert algebras and BL-algebras are obtained.

scholarly journals Two Axiomatizations of Nelson Algebras

2015 ◽  
Vol 23 (2) ◽  
pp. 115-125
Author(s):  
Adam Grabowski
Keyword(s):  
Rough Sets ◽  
Algebraic Model ◽  
Formal Proof ◽  
Boolean Algebras ◽  
Constructive Logic ◽  
Strong Negation ◽  
Binary Operations ◽  
Nelson Algebra ◽  
P 75 ◽  
Nelson Algebras

Nelson algebras were first studied by Rasiowa and Białynicki- Birula [1] under the name N-lattices or quasi-pseudo-Boolean algebras. Later, in investigations by Monteiro and Brignole [3, 4], and [2] the name “Nelson algebras” was adopted - which is now commonly used to show the correspondence with Nelson’s paper [14] on constructive logic with strong negation. By a Nelson algebra we mean an abstract algebra 〈L, T, -, ¬, →, ⇒, ⊔, ⊓〉 where L is the carrier, − is a quasi-complementation (Rasiowa used the sign ~, but in Mizar “−” should be used to follow the approach described in [12] and [10]), ¬ is a weak pseudo-complementation → is weak relative pseudocomplementation and ⇒ is implicative operation. ⊔ and ⊓ are ordinary lattice binary operations of supremum and infimum. In this article we give the definition and basic properties of these algebras according to [16] and [15]. We start with preliminary section on quasi-Boolean algebras (i.e. de Morgan bounded lattices). Later we give the axioms in the form of Mizar adjectives with names corresponding with those in [15]. As our main result we give two axiomatizations (non-equational and equational) and the full formal proof of their equivalence. The second set of equations is rather long but it shows the logical essence of Nelson lattices. This formalization aims at the construction of algebraic model of rough sets [9] in our future submissions. Section 4 contains all items from Th. 1.2 and 1.3 (and the itemization is given in the text). In the fifth section we provide full formal proof of Th. 2.1 p. 75 [16].

scholarly journals Dually hemimorphic semi-Nelson algebras

2019 ◽  
Vol 28 (3) ◽  
pp. 316-340
Author(s):  
Juan Manuel Cornejo ◽  
HernÁn Javier San MartÍn
Keyword(s):  
Heyting Algebras ◽  
Deductive Systems ◽  
Nelson Algebra ◽  
Nelson Algebras ◽  
Lattice Of Congruences

Abstract Extending the relation between semi-Heyting algebras and semi-Nelson algebras to dually hemimorphic semi-Heyting algebras, we introduce and study the variety of dually hemimorphic semi-Nelson algebras and some of its subvarieties. In particular, we prove that the category of dually hemimorphic semi-Heyting algebras is equivalent to the category of dually hemimorphic centered semi-Nelson algebras. We also study the lattice of congruences of a dually hemimorphic semi-Nelson algebra through some of its deductive systems.

Triassic sponges (Sphinctozoa) from Hells Canyon, Oregon

1988 ◽  
Vol 62 (03) ◽  
pp. 419-423 ◽  
Author(s):  
Baba Senowbari-Daryan ◽  
George D. Stanley
Keyword(s):  
Endemic Species ◽  
Upper Triassic ◽  
Island Arc ◽  
Tropical Island ◽  
The Family ◽  
Wallowa Terrane ◽  
Unique Condition ◽  
Hells Canyon

Two Upper Triassic sphinctozoan sponges of the family Sebargasiidae were recovered from silicified residues collected in Hells Canyon, Oregon. These sponges areAmblysiphonellacf.A. steinmanni(Haas), known from the Tethys region, andColospongia whalenin. sp., an endemic species. The latter sponge was placed in the superfamily Porata by Seilacher (1962). The presence of well-preserved cribrate plates in this sponge, in addition to pores of the chamber walls, is a unique condition never before reported in any porate sphinctozoans. Aporate counterparts known primarily from the Triassic Alps have similar cribrate plates but lack the pores in the chamber walls. The sponges from Hells Canyon are associated with abundant bivalves and corals of marked Tethyan affinities and come from a displaced terrane known as the Wallowa Terrane. It was a tropical island arc, suspected to have paleogeographic relationships with Wrangellia; however, these sponges have not yet been found in any other Cordilleran terrane.

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