Small submodules with respect to an arbitrary submodule
نویسندگان
چکیده مقاله:
Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $Tsubseteq X+N$ implies that $Tsubseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.
منابع مشابه
small submodules with respect to an arbitrary submodule
let $r$ be an arbitrary ring and $t$ be a submodule of an $r$-module $m$. a submodule $n$ of $m$ is called $t$-small in $m$ provided for each submodule $x$ of $m$, $tsubseteq x+n$ implies that $tsubseteq x$. we study this mentioned notion which is a generalization of the small submodules and we obtain some related results.
متن کاملOplus-supplemented modules with respect to images of a fully invariant submodule
Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...
متن کاملAnnihilator-small submodules
Let $M_R$ be a module with $S=End(M_R)$. We call a submodule $K$ of $M_R$ annihilator-small if $K+T=M$, $T$ a submodule of $M_R$, implies that $ell_S(T)=0$, where $ell_S$ indicates the left annihilator of $T$ over $S$. The sum $A_R(M)$ of all such submodules of $M_R$ contains the Jacobson radical $Rad(M)$ and the left singular submodule $Z_S(M)$. If $M_R$ is cyclic, then $A_R(M)$ is the unique ...
متن کاملa comparison of teachers and supervisors, with respect to teacher efficacy and reflection
supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...
15 صفحه اولThe Submodule-Based Zero-Divisor Graph with Respect to Some Homomorphism
Let M be an R-module and 0 6= f ∈ M∗ = Hom(M, R). The graph Γf (M) is a graph with vertices Z f (M) = {x ∈ M \ {0} | xf(y) = 0 or yf(x) = 0 for some non-zero y ∈ M}, in which non-zero elements x and y are adjacent provided that xf(y) = 0 or yf(x) = 0, which introduced and studied in [3]. In this paper we associate an undirected submodule based graph ΓfN (M) for each submodule N of M with vertic...
متن کاملType and cotype with respect to arbitrary orthonormal systems
Mathematisches Institut der Friedrich Schiller Universita̋t Jena UHH 17. OG D O7743 Jena Germany E-mail: [email protected] Mathematisches Seminar der Universita̋t Kiel Ludewig Meyn Strasse 4 D 24098 KIEL Germany E-mail: [email protected] Abstract Let Φ = (φk)k∈IN be an orthonormal system on some σ-finite measure space (Ω, p). We study the notion of cotype with respect to Φ...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 3 شماره 2
صفحات 43- 51
تاریخ انتشار 2015-12-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023