This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that functions as an act over S if and only if functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following, is acting over S if and only if is a module where T is a nilpotent operator, is a faithful act over S, where T is any bounded linear operator, if T is any bounded operator, then is separated, if is separated act over S, Then T is injective, if a basis K = {vj, j} for V, then every element w of can be composed as =(pn (T) + . v, for some v in V, and put T as similar to any operator from to and V as a finite dimensional normed space, then is Noetherian act over S if S is Noetherian.
In this paper, the Normality set will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of .
The aim of this paper is to introduce the definition of projective 3-space over Galois field GF(q), q = pm, for some prime number p and some integer m.
Also the definitions of (k,n)-arcs, complete arcs, n-secants, the index of the point and the projectively equivalent arcs are given.
Moreover some theorems about these notations are proved.
In this paper, we introduce the bi-normality set, denoted by , which is an extension of the normality set, denoted by for any operators in the Banach algebra . Furthermore, we show some interesting properties and remarkable results. Finally, we prove that it is not invariant via some transpose linear operators.
In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.
In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.
In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact
... Show MoreA complex number is called an extended eigenvalue for an operator on a Hilbert space H if there exists a nonzero operator such that: such is called an extended eigenoperator corresponding to. The goal of this paper is to calculate extended eigenvalues and extended eigenoperators for the weighted unilateral (Forward and Backward) shift operators. We also find an extended eigenvalues for weighted bilateral shift operator. Moreover, the closedness of extended eigenvalues for the weighted unilateral (Forward and Backward) shift operators under multiplication is proven.
Let R be a commutative ring with identity, and let M be a unitary (left) R- modul e. The ideal annRM = {r E R;rm = 0 V mE M} plays a central
role in our work. In fact, we shall be concemed with the case where annR1i1 = annR(x) for some x EM such modules will be called bounded modules.[t htrns out that there are many classes of modules properly contained in the class of bounded modules such as cyclic modules, torsion -G·ee modulcs,faithful multiplicat
... Show MoreThe concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.
The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.