Some Results on Coatoms and Comolecules in BL-Algebras

In this paper, some new properties and results of coatoms and comolecules in BL-algebras are given. Also, the notion of a strong coatom in BL-algberas, is defined and investigated. </jats:p

t-PRIME SUBMODULES

Let R be a commutative ring with identity. For t is an element of N, a proper submodule N of an R-module M is called a t-prime submodule if rm is an element of N (r is an element of R, m is an element of M), then m is an element of N or r(t) is an element of(N :(R) M). We show that any maximal t-prime submodule, with respect to inclusion, is prime and a proper submodule is a t-prime submodule if and only if its quotient module is t-torsion free. We obtain some characterizations of t-prime submodules. Also various properties of t-prime submodules are investigated. We provide several examples which illustrate our results

Primary Filters in BL-algebras

In this paper, we defined the prime-like filters of [Formula: see text]-algebras, and proved some relations between this filter and other types of filters in [Formula: see text]-algebras. Also, we found the relation between prime-like filters and constructed the quotient [Formula: see text]-algebras via this filter. We proved some results that have proven for prime filters of [Formula: see text]-algebras, to the case of prime-like filters of [Formula: see text]-algebras. In this way, we found new properties for the primary filters of [Formula: see text]-algebras. Also, we introduced the notions of prime-like [Formula: see text]-algebras ([Formula: see text]-algebras), and Top-like [Formula: see text]-algebras. And we applied the notion of prime-like filters to define and study a new topology on [Formula: see text]-algebras.</jats:p

On nn-submodules and G.nG.n-submodules

summary:We investigate some properties of $n$-submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an $n$-submodule. Also, we show that if $M$ is a finitely generated $R$-module and $\sqrt {{{\rm Ann} }_R(M)}$ is a prime ideal of $R$, then $M$ has $n$-submodule. Moreover, we define the notion of \hbox {$G.n$-submodule}, which is a generalization of the notion of $n$-submodule. We find some characterizations of $G.n$-submodules and we examine the way the aforementioned notions are related to each other

T-quasi continuous modules

In this paper, we investigate the t-quasi continuous property for modules. It is proved that M is t-quasi continuous, if and only if M is a direct sum of a Z2-torsion module and a quasi-continuos module. Moreover we characterize the rings R for which certain R-modules are t-quasi continuous. We show that every R-module is t-quasi continuous, if and only if R(N) is t-quasi continuous, if and only if everyfree R-module is t-quasi continuous.Key words: Continuous modules, quasi-continuous modules, T-continuous modules, T-quasi continuous modules, T-extending module