Generalizations of Knopp ’ S Identity
نویسندگان
چکیده
For integers a, b and n > 0 we define
منابع مشابه
Some remarks on generalizations of classical prime submodules
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $phi:S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$phi$-classical prime submodule, if whenever $r_{1},ldots,r_{n-1}in R$ and $min M$ with $r_{1}ldots r_{n-1}min Nsetminusphi(N)$, then $r_{1...
متن کاملUnity within Diversity: Foundations and Dynamics of National Identity in Iran
The article provides a critical assessment of the more recent literature that relies on theoretical frameworks such as post modernism and globalization to deal with national identity, ethnicity and cultural mobility. Explaining sensitive and complicated issues such as identity requires the extensive use of the native historical, cultural and sociological sources related to the Iranian experienc...
متن کاملOn two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective
Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...
متن کاملSOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS
Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-kno...
متن کاملGENERALIZATIONS OF MCSHANE ’ S IDENTITY TO HYPERBOLIC CONE - SURFACES 3 Theorem 1
We generalize McShane’s identity for the length series of simple closed geodesics on a cusped hyperbolic surface [17] to hyperbolic cone-surfaces (with all cone angles ≤ π), possibly with cusps and/or geodesic boundary. In particular, by applying the generalized identity to the orbifolds obtained from taking the quotient of the one-holed torus by its elliptic involution, and the closed genus tw...
متن کامل