Results 1 to 10 of about 29 (23)
NeutroAlgebra & AntiAlgebra vs. Classical Algebra [PDF]
Transactions on Fuzzy Sets and Systems, 2022 NeutroAlgebra $\&$ AntiAlgebra vs. Classical Algebra is a like Realism vs. Idealism. Classical Algebra does not leave room for partially true axioms nor partially well-defined operations. Our world is full of indeterminate (unclear, conflicting
Florentin Smarandache
doaj +2 more sources
A Study of NeutroAlgebra and AntiAlgebra of Ideals in a Factor Ring [PDF]
Neutrosophic Sets and Systems, 2023 If I is an ideal in a ring R and M is the collection of all nontrivial ideals in the factor ring R/I, we find in this paper conditions under which (M, ⊕), (M, ⊗) and (M, ∩) are NeutroAlgebras and AntiAlgebras where ⊕, ⊗ and ∩ are the usual sum, product ...
A.A.A. Agboola, M.A. Ibrahim
doaj +3 more sources
Lie antialgebras: Prémices [PDF]
Journal of Algebra, 2011 The main purpose of this work is to develop the basic notions of the Lie theory for commutative algebras. We introduce a class of $\mathbbZ_2$-graded commutative but not associative algebras that we call ``Lie antialgebras''. These algebras are closely related to Lie (super)algebras and, in some sense, link together commutative and Lie algebras.
Zhang, Tao, Zhang, Heyu
+13 more sources
NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries [PDF]
Neutrosophic Sets and Systems, 2021 In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry.
Florentin Smarandache
doaj +1 more source
Crossed modules for Hom–Lie antialgebras [PDF]
Journal of Algebra and Its Applications, 2021 In this paper, we introduced the concept of crossed modules for Hom–Lie antialgebras. It is proved that the category of crossed modules for Hom–Lie antialgebras and the category of [Formula: see text]-Hom–Lie antialgebras are equivalent to each other.
Tao Zhang, Heyu Zhang
openaire +3 more sources
A note on AntiGeometry and NeutroGeometry and their application to real life [PDF]
Neutrosophic Sets and Systems, 2022 Dealing with NeutroGeometry in true, false, and uncertain regions is becoming of great interested for researchers. Not too many studies have been done on this topic, for that reason, aim of this work is to define a new method to deal with NeutroGeometry ...
Carlos Granados
doaj +1 more source
Real Examples of NeutroGeometry & AntiGeometry [PDF]
Neutrosophic Sets and Systems, 2023 For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only
Florentin Smarandache
doaj +1 more source
NeutroAlgebra of Idempotents in Group Rings [PDF]
Neutrosophic Sets and Systems, 2022 In this paper, the authors study the new concept of NeutroAlgebra of idempotents in group rings. It is assumed that RG is the group ring of a group G over the ring R. R should be a commutative ring with unit 1.
Vasantha Kandasamy +1 more
doaj +1 more source
Generalizations and alternatives of classical algebraic structures to neutroAlgebraic structures and antiAlgebraic structures [PDF]
Journal of Fuzzy Extension and Applications, 2020 In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are ...
Florentin Smarandache
doaj +1 more source
NeutroAlgebra of Neutrosophic Triplets using {Zn, ×} [PDF]
Neutrosophic Sets and Systems, 2020 Smarandache in 2019 has generalized the algebraic structures to NeutroAlgebraic structures and AntiAlgebraic structures. In this paper, authors, for the first time, define the NeutroAlgebra of neutrosophic triplets group under usual+ and x, built using ...
Vasantha Kandasamy +2 more
doaj +1 more source