Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHarmanci Injectivity of Modules
55
0
0.0
(
0
)
Authors
Burcu Ungor
Ask ChatGPT about the research
No Arabic abstract
In this paper, we are interested in a class of modules partaking in the hierarchy of injective and cotorsion modules, so-called Harmanci injective modules, which turn out by the motivation of relations among the concepts of injectivity, flatness and cotorsionness. We give some characterizations and properties of this class of modules. It is shown that the class of all Harmanci injective modules is enveloping, and forms a perfect cotorsion theory with the class of modules whose character modules are Matlis injective. One of the main objectives we pursue is to know when the injective envelope of a ring as a module over itself is a flat module.
rate research
Read More
Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S=$ End$_R(M)$. In this paper we introduce $pi$-Rickart modules as a generalization of generalized right principally projective rings as well as that of Rickart modules. The module $M$ is called {it $pi$-Rickart} if for any $fin S$, there exist $e^2=ein S$ and a positive integer $n$ such that $r_M(f^n)=eM$. We prove that several results of Rickart modules can be extended to $pi$-Rickart modules for this general settings, and investigate relations between a $pi$-Rickart module and its endomorphism ring.
In this paper, we define the induced modules of Lie algebra ad$(B)$ associated with a 3-Lie algebra $B$-module, and study the relation between 3-Lie algebra $A_{omega}^{delta}$-modules and induced modules of inner derivation algebra ad$(A_{omega}^{delta})$. We construct two infinite dimensional intermediate series modules of 3-Lie algebra $A_{omega}^{delta}$, and two infinite dimensional modules $(V, psi_{lambdamu})$ and $(V, phi_{mu})$ of the Lie algebra ad$(A_{omega}^{delta})$, and prove that only $(V, psi_{lambda0})$ and $(V, psi_{lambda1})$ are induced modules.
It is proved that if A_p is a countable elementary abelian p-group, then: (i) The ring End(A_p) does not admit a nondiscrete locally compact ring topology. (ii) Under (CH) the simple ring End(A_p)/I, where I is the ideal of End(A_p) consisting of all endomorphisms with finite images, does not admit a nondiscrete locally compact ring topology. (iii) The finite topology on End(A_p) is the only second metrizable ring topology on it. Moreover, a characterization of completely simple endomorphism rings of the endomorphism rings of modules over commutative rings is also obtained.
It is proved that localizations of injective $R$-modules of finite Goldie dimension are injective if $R$ is an arithmetical ring satisfying the following condition: for every maximal ideal $P$, $R_P$ is either coherent or not semicoherent. If, in addition, each finitely generated $R$-module has finite Goldie dimension, then localizations of finitely injective $R$-modules are finitely injective too. Moreover, if $R$ is a Prufer domain of finite character, localizations of injective $R$-modules are injective.
In this paper we give some relationships among the Groebner-Shirshov bases in free associative algebras, free left modules and double-free left modules (free modules over a free algebra). We give the Chibrikovs Composition-Diamond lemma for modules and show that Kang-Lees Composition-Diamond lemma follows from this lemma. As applications, we also deal with highest weight module over the Lie algebra $sl_2$, Verma module over a Kac-Moody algebra, Verma module over Lie algebra of coefficients of a free conformal algebra and the universal enveloping module for a Sabinin algebra.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
