In this paper, we present necessary and sufficient conditions for X? to be idempotent orthogonal idempotent, where ? {A?, AD, AD?, A?,D Aw}. Several characteristics when is are derived by core-EP decomposition. Additionally, give some equivalent matrix A using the properties of generalized inverses A.

Combining the definition of 0-Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0-Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine their idempotents and show that they are J -trivial. For type A we show that Catalan numbers appear as the maximal cardinality of our monoids, in which case ...

Let Xn be the finite set {1,2,3· · ·, n} and On defined by On={α∈Tn:(∀x, y∈Xn), x⩽y→xα⩽yα}be semigroup of full order-preserving mapping on Xn. A transformation α in is called quasi-idempotent if α=α2=α4. We characterise show that generated. Moreover, we obtained an upper bound forquasi-idempotents rank On, is, showed cardinality a minimum quasi-idempotents generating for less than or equal to ⌈...

The notion of Abelian kernel of a finite monoid extends the notion of derived subgroup of a finite group. In this line, an extension of the notion of solvable group to monoids is quite natural: they are the monoids such that the chain of Abelian kernels ends with the submonoid generated by the idempotents. We prove in this paper that the finite idempotent commuting monoids satisfying this prope...

Let S be a left amenable semigroup. Say that a subset A of S is large if there is some left invariant mean μ on S with μ(χA) > 0. A subset B of S is density recurrent if and only if, whenever A is a large subset of S, there is some x ∈ B such that x−1A ∩ A is large. We show that the set DR(S) of ultrafilters on S, every member of which is density recurrent, is a compact subsemigroup of the Ston...

design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. these include techniques for designing non-separable multidimensional paraunitary matrices. properties of the structures are obtained and proofs given. paraunitary matrices play a central role in signal processing, in particular in the areas of filterbanks and wavelets.

We exhibit the primitive central idempotents of a semisimple group algebra of a finite nilpotent group over an arbitrary field (without using group characters), examining the abelian case separately. Our result extends and improves the main result in [1].