If (R,M) and (S,N) are quasilocal (commutative integral) domains and f : R → S is a (unital) ring homomorphism, then f is said to be a strong local homomorphism (resp., radical local homomorphism) if f (M) = N (resp., f (M) ⊆ N and for each x ∈ N , there exists a positive integer t such that xt ∈ f (M)). It is known that if f : R→ S is a strong local homomorphism where R is a pseudovaluation do...

Let $f:A\rightarrow B$ be a ring homomorphism and $K$ an ideal of $B$. Many variations the notions clean nil-clean rings have been studied by variety authors. We investigate strongly $\pi$-regular clean-like properties amalgamation $A\bowtie^{f}K$ $A$ with $B$ along respect to $f$.

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in commutative rings. Let \(G\) be a group \(R\) \(G\)-graded ring with nonzero identity \(1\neq0\). A proper ideal \(P\) of is called if for each nonunits \(x,y,z\in h(R)\) \(0\neq xyz\in P\), then either \(xy\in P\) or \(z\in P\). We give many properties characterizations ideals. Moreover, investigate under homomorph...

In this paper, we study some of the properties of (Q, L) -fuzzy normal ideal of a ring and prove some results on these. 2000 AMS SUBJECT CLASSIFICATION: 03F55, 08A72, 20N25.

Let A and B be unital rings. An additive map T:A→B is called a weighted Jordan homomorphism if c=T(1) an invertible central element cT(x2)=T(x)2 for all x∈A. We provide assumptions, which are in particular fulfilled when A=B=Mn(R) with n≥2 R any ring 12, under every surjective the property that T(x)T(y)+T(y)T(x)=0 whenever xy = yx 0 homomorphism. Further, we show prime char(A)≠2,3,5, then bijec...

Let (R,m) denote an n-dimensional Gorenstein ring. For an ideal I ⊂ R of height c we are interested in the endomorphism ring B = HomR(H c I (R),H c I (R)). It turns out that B is a commutative ring. In the case of (R, m) a regular local ring containing a field B is a Cohen-Macaulay ring. Its properties are related to the highest Lyubeznik number l = dimk Ext d R(k, H c I (R)). In particular R ≃...

multi fuzzy set theory is an extension of theory, which deals with the dimensional fuzziness. In this paper, we introduce concepts multi-fuzzy rings, ideal, image multi- ideal a ring under homomorphism, Cartesian product set, and some related properties theorems are investigated. The purpose study to implement rings in rings.

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...