Let [Formula: see text] be a ring, class of text]-modules and an integer. We introduce the concepts Gorenstein text]-[Formula: text]-injective text]-flat modules via special finitely presented modules. Besides, we obtain some equivalent properties these on text]-coherent rings. Then investigate relations among text]-injective, text]-flat, injective flat text]-rings (i.e., self rings). Several k...

in this paper, two new hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. it is shown that finite screw motions in minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual lorentzian space. moreover, by means of hamilton operators, screwmotion is obtained in 3-dimensional minkowski space 3r1

We prove a factorization of completely bounded maps from a C *-algebra A (or an exact operator space E ⊂ A) to ℓ 2 equipped with the operator space structure of (C, R) θ (0 < θ < 1) obtained by complex interpolation between the column and row Hilbert spaces. More precisely, if F denotes ℓ 2 equipped with the operator space structure of (C, R) θ , then u : A → F is completely bounded iff there a...

$R$-module. In this paper, we explore more properties of $Max$-injective modules and we study some conditions under which the maximal spectrum of $M$ is a $Max$-spectral space for its Zariski topology.

We describe how self-adjoint ordered operator spaces, also called non-unital systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. explain this perspective has several advantages over other notions of literature. In particular, category includes injective objects and Webster-Winkler-type duality theorem, both which we show generally fail syste...

We suggest new dual algorithms and iterative methods for solving monotone generalized variational inequalities. Instead of working on the primal space, this method performs a dual step on the dual space by using the dual gap function. Under the suitable conditions, we prove the convergence of the proposed algorithms and estimate their complexity to reach an ε-solution. Some preliminary computat...

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any rest...

Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional $1$-injective Banach space contains a hyperplane is $(2+\varepsilon )$-injective for $\varepsilon \gt 0$, yet not $2$-injective, rem