first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

In a commutative Noetherian local complex normed algebra which is complete in its M-adic metric there are only finitely many closed prime ideals.

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

A generalized BL-algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities x ∧ y = ((x ∧ y)/y)y = y(y\(x∧ y)). It is shown that all finite GBL-algebras are commutative, hence they can be constructed by iterating ordinal sums and direct products of Wajsberg hoops. We also observe that the idempotents in a GBL-algebra form a subalgebra of elements that commute with ...

Segal’s chronometry is based on a space–time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). There are exactly two more non-commutative four-dimensional Lie algebras that admit such a form. They determine space–times L and F. The world F is based on the Lie algebra u(1,1), in terms of which the pseudo-Hermitian rea...

We introduce the notion of a graded integral element, prove the counterpart of the lying-over theorem on commutative algebra in the context of left commutative rngs, and use the Hu-Liu product to select a class of noncommutative rings. Left commutative rngs were introduced in [1]. I have two reasons to be interested in left commutative rngs. The first reason is that left commutative rngs are a ...

Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...