In this study, we define the concept of an ω-fuzzy set subring and show that intersection two subrings is also a given ring. Moreover, give notion ideal investigate different fundamental results phenomenon. We extend ideology to propose coset develop quotient ring with respect particular fuzzy analog into classical Additionally, found subring. idea support prove various important characteristic...

In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCCideals in BCC-algebras is introd...

For every local ring R in what follows, mR denotes the maximal ideal. Let Λ̃ be a complete, regular, local Noetherian ring, let E ⊂ m Λ̃ be an ideal, and denote the quotient by Λ. Thus, Λ is also a complete, local Noetherian ring. Denote the residue field Λ/mΛ by k. Denote by C = CΛ the category whose objects are Λ-algebras A such that (i) A is a local, Artin ring with mΛA ⊂ mA, and (ii) the indu...

The Zykov ring of signed finite simple graphs with topological join as addition and compatible multiplication is an integral domain but not a unique factorization domain. We know that because by the graph complement operation it is isomorphic to the strong Sabidussi ring with disjoint union as addition. We prove that the Euler characteristic is a ring homomorphism from the strong ring to the in...

An algorithm is presented that allows to multiply two univariate polynomials of degree no more than n with coefficients from an arbitrary (possibly non-commutative) ring in O(n log(n) log(log n)) additions and subtractions and O(n log(n)) multiplications. The arithmetic depth of the algorithm is O(log(n)). This algorithm is a modification of the Schönhage-Strassen procedure to arbitrary radix f...

Let be a commutative ring with 1 and left unitary . In this papers we introduced studied concept P-small compressible (An is said to if can embedded in every of it nonzero submodule Equivalently, there exists monomorphism , retractable for non-zero homomorphism whenever as generalization respectively give some their advantages characterizations examples.

A geometric graph G is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. Two geometric realizations of a simple graph are geo-isomorphic if there is a vertex bijection between them that preserves vertex adjacencies and non-adjacencies, as well as edge crossings and non-crossings. A natural extension of graph homomorphisms, geo-homomo...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of P, where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is related to the coordi...

Summary We formalize in the Mizar system [3], [4] some basic properties on left module over a ring such as constructing via of endomorphism an abelian group and set all homomorphisms modules form [1] along with Ch. 2 set. 1 [2]. The formalized items are shown below list notations: M ab for Abelian suffix “ ” without is used ring. 1. denoted by End ( ). 2. A pair homomorphism <m:math xmlns:m="ht...

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring B(X,L, σ), which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent i...