Results 1 to 10 of about 215 (48)
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
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 +6 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
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Lie antialgebras: premices [PDF]
Journal of Algebra, 2009 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''.
Ovsienko, Valentin
core +7 more sources
Lie antialgebras: cohomology and representations [PDF]
AIP Conference Proceedings, 2008 We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations.
Anatol Odzijewicz +4 more
core +3 more sources
Universal Enveloping Algebras of Lie Antialgebras [PDF]
Algebras and Representation Theory, 2010 Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its properties.
Leidwanger, Séverine +1 more
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Odd Jacobi manifolds and Loday-Poisson brackets
Journal of Mathematics, Volume 2014, Issue 1, 2014., 2013 In this paper we construct a non-skewsymmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets.
Bruce, Andrew James
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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
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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
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