Today, literature and poetry have a more comprehensive definition than mere literary expression with academic meanings and tools. Literature is the collection of all the scientific abilities of the language in the field of structure and richness. The artistic creativity of the poet and the employment of excellent compositions and themes lead to the production of a literary and artistic work, which can be found in the excitement and expansion of the audience. The aim of this research is to reach the communication network of all the factors related to the language and the appearance of the word, which not only carries the meaning, but also creates a different meaning and concept from the apparent meaning that results from the phonetic, lexical or visual mechanism. A network that is referred to as "artwork". Artistic device (prime) is a meta-array approach to the aesthetic tools of language in poetry, which formalists consider to be the art of alienating language from the mind of the audience.

In this paper we introduced the concept of minimal prime filters in commutative BE-algebras. A characterization theorem for minimal prime filters of BE-algebras is derived. Some properties of minimal prime filters of a commutative BE-algebras are derived with the help of congruences. A necessary and sufficient is derived for a pair of minimal prime filters to become co-maximal.

In this paper , the concepts of weakly prime filters and super-max filters in $\mathrm{BL}$-algebras are introduced , and the relationships between them are discussed . Also , some properties and relations between these filters and other types of filters in $\mathrm{BL}$-algebras are given . With some examples , it is shown that these filters have differences . After that , the notions of weakly linear $\mathrm{BL}$-algebras and weak top $\mathrm{BL}$-algebras are defined and investigated . Finally , using the notion of a weakly prime filter , a new topology on $\mathrm{BL}$-algebras is defined and studied .

The notion of ω,-filters is introduced in distributive lattices and their properties are studied. A set of equivalent conditions is derived for every maximal filter of a distributive lattice to become an ω,-filter which leads to a characterization of quasi-complemented lattices. Some sufficient conditions are derived for proper D-filters of a distributive lattice to become an ω,-filter. Finally, ω,-filters of a distributive lattice are characterized with the help of minimal prime D-filters.

In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial ∨-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology.

Let R be a commutative ring with identity. A proper ideal P of R is an (n - 1, n)-Fm-prime ((n - 1, n)-weakly prime) ideal if a1, … , anÎR, a1 … anÎP\P m (a1 … anÎP\{0}) implies a1 … ai-1 ai+1 … anÎP, for some iÎ{1, …, n}; (m, n³2).In this paper several results concerning (n - 1, n)-Fm-prime and (n - 1, n)-weakly prime ideals are proved. We show that in a Noetherian domain a Fm-prime ideal is primary and we show that in some well-known rings (n - 1, n)-Fm-prime ideals and (n - 1, n)-prime ideals coincide.

In this paper, by considering the notions of maximal, prime, and minimal prime filters in residual lattices, we study their properties and some examples of residuated lattices are given. It is reminded first the notion of a filter of a residuated lattice and then we show that each proper filter is contained in a maximal filter and therefore in a prime filter. We investigate the prime filters in an MTL algebra and state and prove the fundamental theorem of the prime filters for residuated lattices. We investigate the residuated lattices in which each its filter is principal, and by using the prime filters, we inspect co-annihilators. Then the notion of a minimal prime filter in a residuated lattice is introduced and a fundamental theorem for minimal prime filters in residuated lattice is stated and proved. Finally, we introduce the divisor filters in a residuated lattice and by using them,we investigate the minimal prime filters.