The concept of right (left) quotient (or residual) of an ideal η by anideal ν of an L-subring μ of a ring R is introduced. The right (left) quotients areshown to be ideals of μ . It is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an L-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . Most of the results pertaining to the notion of quotients(or residual) of ...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

In this paper, we used tetranuclear copper (II) Schiff base complexes, [Cu4 (μ-sal2hn) (μ-N3)2(N3)2] (1) and [Cu4 (μ-salophen) (μ1, 1-N3)2(N3)2] (2), as new precursor in solid-state thermal decomposition for the synthesis of CuO ...

Background: Attenuation coefficient (μ) plays an important role in calculations of treatment planning systems, as well as determination of dose distributions in external beam therapy, dosimetry, protection, phantom materials and industry. So, its exact measurement or calculation is very important. The aim of this study was to evaluate the μ in different points in the water phantom anal...

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...

Synthesis of a natural proline-rich cyclopolypeptide - rolloamide A [8] was carried out by coupling of tri- and tetrapeptide units Boc-Phe-Pro-Val-OMe and Boc-Pro-Leu-Pro-Ile-OMe after proper deprotection at carboxyl and amino terminals using carbodiimide chemistry in alkaline environment followed by cyclization of linear heptapeptide segment in the presence of base. The structure of synthesize...

Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-1<...