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Idempotents --- Tropical geometry --- Mathematical physics

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The study of idempotent elements in group algebras (or, more generally, the study of classes in the K-theory of such algebras) originates from geometric and analytic considerations. For example, C.T.C. Wall [72] has shown that the problem of deciding whether a ?nitely dominated space with fundamental group? is homotopy equivalent to a ?nite CW-complex leads naturally to the study of a certain class in the reduced K-theoryK (Z?) of the group ringZ?. 0 As another example, consider a discrete groupG which acts freely, properly discontinuously, cocompactly and isometrically on a Riemannian manifold. Then, following A. Connes and H. Moscovici [16], the index of an invariant 0th-order elliptic pseudo-di?erential operator is de?ned as an element in the ? ? K -group of the reduced groupC -algebraCG. 0 r Theidempotentconjecture(alsoknownasthegeneralizedKadisonconjec- ? ? ture) asserts that the reduced groupC -algebraCG of a discrete torsion-free r groupG has no idempotents =0,1; this claim is known to be a consequence of a far-reaching conjecture of P. Baum and A. Connes [6]. Alternatively, one mayapproachtheidempotentconjectureasanassertionabouttheconnect- ness of a non-commutative space;ifG is a discrete torsion-free abelian group ? thenCG is the algebra of continuous complex-valued functions on the dual r

Idempotents. --- Matrices. --- Group algebras. --- Algebras, Group --- Abelian groups --- Locally compact groups --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Idempotent elements --- Algebras, Linear --- Mathematical physics --- Algebra. --- K-theory. --- Group theory. --- Functional analysis. --- Associative Rings and Algebras. --- Category Theory, Homological Algebra. --- K-Theory. --- Group Theory and Generalizations. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic topology --- Homology theory --- Mathematics --- Mathematical analysis --- Associative rings. --- Rings (Algebra). --- Category theory (Mathematics). --- Homological algebra. --- Homological algebra --- Category theory (Mathematics) --- Algebra, Homological --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)

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This book contains 37 papers by 73 renowned experts from 13 countries around the world, on following topics: neutrosophic set; neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup and hypergroup; neutrosophic offset; uninorm; neutrosophic offuninorm and offnorm; neutrosophic offconorm; implicator; prospector; n-person cooperative game; ordinary single-valued neutrosophic (co)topology; ordinary single-valued neutrosophic subspace; ?-level; ordinary single-valued neutrosophic neighborhood system; ordinary single-valued neutrosophic base and subbase; fuzzy numbers; neutrosophic numbers; neutrosophic symmetric scenarios; performance indicators; financial assets; neutrosophic extended triplet group; neutrosophic quadruple numbers; refined neutrosophic numbers; refined neutrosophic quadruple numbers; multigranulation neutrosophic rough set; nondual; two universes; multiattribute group decision making; nonstandard analysis; extended nonstandard analysis; monad; binad; left monad closed to the right; right monad closed to the left; pierced binad; unpierced binad; nonstandard neutrosophic mobinad set; neutrosophic topology; nonstandard neutrosophic topology; visual tracking; neutrosophic weight; objectness; weighted multiple instance learning; neutrosophic triangular norms; residuated lattices; representable neutrosophic t-norms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ?-distributive; probabilistic neutrosophic hesitant fuzzy set; decision-making; Choquet integral; e-marketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.

nonstandard neutrosophic supremum --- classical statistics --- complex neutrosophic set --- neutrosophic offnorm --- neutrosophic extended triplet group --- multi-attribute decision-making (MADM) --- neutrosophic time series --- refined neutrosophic quadruple numbers --- BNHHA aggregation operator --- neutrosophic offconorm --- monad --- matrix representation --- left monad closed to the right --- implicator --- neutrsophic set --- neutrosophic correlation --- neutrosophic cubic sets --- decision-making --- MoBiNad set --- open and closed monads to the left/right --- distance measure --- De Morgan neutrosophic triples --- group decision making --- financial assets --- soft expert set --- uninorm --- multi-attribute group decision making --- sampling plan --- cubic sets --- neutrosophic cubic ordered weighted geometric operator (NCOWG) --- shale gas water management system --- weighted average operator --- aggregation operations --- quality function deployment --- Einstein t-norm --- neutrosophic rings --- non-standard neutrosophic topology --- BNHWA aggregation operator --- hypergroup --- triangular neutrosophic cubic fuzzy number --- pierced and unpierced binads --- numerical application --- neutrosophic cubic weighted geometric operator (NCWG) --- relations --- extended nonstandard analysis --- arithmetic averaging operator --- nonstandard reals --- Choquet integral --- Function approximation --- neutrosophic triangular norms --- weighted geometric operator --- neutrosophic regression --- optimization solution --- ordinary single valued neutrosophic neighborhood system --- smart port --- neutrosophic topology --- multi-criteria decision making techniques --- low-carbon supplier selection --- producer’s risk --- quasi-completely regular semigroup --- score function --- MAGDM --- multicriteria decision-making --- neutrosophic soft rough --- NET-hypergroup --- refined neutrosophic numbers --- neutrosophic logical relationship groups --- combined weighted average --- TOPSIS --- neutrosophic logical relationship --- logarithmic aggregation operators --- non-standard analysis --- multi-attribute decision-making --- neutrosophic extended triplet semihypergroup (NET-semihypergroup) --- aggregation --- nonstandard neutrosophic logic --- symmetric relation --- uncertainty modeling --- single valued neutrosophic sets --- BNHOWA aggregation operator --- ordinary single valued neutrosophic subspace --- generalized neutrosophic extended triplet group --- multi-attribute decision making --- ordinary single valued neutrosophic base --- nonstandard arithmetic operations --- pierced binad --- MCGDM problems --- simplified neutrosophic set --- residuated lattices --- Neutrosophic compound orthogonal neural network --- rough set approximation --- single-valued neutrosophic linguistic set --- binad --- multi-granulation neutrosophic rough set --- single valued neutrosophic set --- infinitesimals --- standard reals --- soft set --- non-standard neutrosophic mobinad set --- certainty function --- neutrosophic weight --- two universes --- sample size --- n-person cooperative game --- paper defect diagnosis --- performance indicators --- semihypergroup --- logarithmic operational laws --- right monad closed to the left --- idempotents --- unpierced binad --- neutrosophic cubic hybrid weighted arithmetic and geometric aggregation operator (NCHWAGA) --- neutrosophic symmetric scenarios --- extended nonstandard neutrosophic logic --- neutrosophic statistics --- neutrosophic goal programming approach --- neutrosophic offset --- neutrosophic statistical interval method --- weighted multiple instance learning --- neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) --- fuzzy parameterized single valued neutrosophic soft expert set --- single-valued neutrosophic soft number and its operations --- Internet of Things --- extended non-standard analysis --- dietary fat level --- soft sets --- visual tracking --- neutrosophic offuninorm --- neutrosophic cubic Einstein weighted geometric operator (NCEWG) --- ordinary single valued neutrosophic subbase --- membership function --- non-dual --- SVN soft weighted arithmetic averaging operator --- Q-neutrosophic set --- neutrosophic sets --- fuzzy numbers --- intuitionistic fuzzy parameters --- producer’s risk’ --- graph representation --- exponential similarity measure --- infinities --- maximizing deviation --- Multi-attribute decision making --- SVN soft weighted geometric averaging operator --- objectness --- Q-neutrosophic soft set --- accuracy function --- consumer’s risk --- decision making --- Neutrosophic number --- clifford semigroup --- neutrosophic numbers --- neutrosophic residual implications --- nonstandard neutrosophic lattices of first type (as poset) and second type (as algebraic structure) --- covering --- e-marketing --- nonstandard analysis --- neutrosophic quadruple rings --- complex neutrosophic soft expert set --- single-valued neutrosophic set --- neutrosophic cubic soft expert system --- neutrosophic cubic soft sets --- triangular neutrosophic number --- supply chain sustainability metrics --- neutrosophic quadruple numbers --- ?-level --- nonstandard neutrosophic infimum --- infinitely ?-distributive --- plithogeny --- neutrosophic set --- fuzzy logic --- prospector --- Neutrosophic function --- representable neutrosophic t-norms --- probabilistic neutrosophic hesitant fuzzy set (PNHFS) --- prostate cancer --- nonstandard unit interval --- port evaluation --- simplified neutrosophic hesitant fuzzy set --- ordinary single valued neutrosophic (co)topology