Second and Secondary Lattice Modules
نویسندگان
چکیده
Let M be a lattice module over the multiplicative lattice L. A nonzero L-lattice module M is called second if for each a ∈ L, a1M = 1M or a1M = 0M . A nonzero L-lattice module M is called secondary if for each a ∈ L, a1M = 1M or a(n)1M = 0 M for some n > 0. Our objective is to investigative properties of second and secondary lattice modules.
منابع مشابه
Uniformly Secondary Modules over Commutative Ring
In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.
متن کاملA Note on Artinian Primes and Second Modules
Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.
متن کاملThe secondary radicals of submodules
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual o...
متن کاملModules with Noetherian second spectrum
Let $R$ be a commutative ring and let $M$ be an $R$-module. In this article, we introduce the concept of the Zariski socles of submodules of $M$ and investigate their properties. Also we study modules with Noetherian second spectrum and obtain some related results.
متن کاملThe categories of lattice-valued maps, equalities, free objects, and $mathcal C$-reticulation
In this paper, we study the concept of $mathcal C$-reticulation for the category $mathcal C$ whose objects are lattice-valued maps. The relation between the free objects in $mathcal C$ and the $mathcal C$-reticulation of rings and modules is discussed. Also, a method to construct $mathcal C$-reticulation is presented, in the case where $mathcal C$ is equational. Some relations between the conce...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
دوره 2014 شماره
صفحات -
تاریخ انتشار 2014