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Using a new definition, with respect to [21], for normal hyperideals in Krasner (m, n)-hyperrings, we show that the corresponding quotient structures are (m, n)-rings. We prove equivalency of (strongly) regular and (strongly) compatible relations on n-ary hypergroups. Also, the connection between (m, n)-hyperfields and maximal normal hyperideals is investigated.

In this paper we introduce and study distributive elements, dual distributive elements in hyperlattices, and prove that these elements forms ∧-semi lattice and ∨-semi hyperlattice, respectively. We use the properties of prime ideals and prime filters in hyperlattices. We will proceed to introduce the notion of dual distributive hyperlattices, I-filters and filters generated by dual distributive elements. Finally, the relationship between good homomorphisms and istributive (resp. dual distributive)elements in hyperlattices are investigated.

The purpose of this paper is the study of prime ideals and prime filters in hyperlattices. I-filter and the filter generated by a ∈ L are introduced. Moreover, we introduce dual distributive hyperlattices, and I-filter in dual distributive hyperlattices. Some properties of hyperlat- tices are studied and the relationship between prime ideals and prime filters in hyperlattices is discussed.

In this paper, we discuss some questions about Krasner hyperrings and Krasner hypermodules. In this regard, we introduce some classes of Krasner hypermodules and obtain some results to give some approaches to answer the questions. Finally, we state some open problems as the enriched version of the questions. [ABSTRACT FROM AUTHOR]

We introduce and study regular multiplicative hyperrings, as a generalization of classical rings. Also, we use the fundamental relation γ* on a given regular multiplicative hyperring R and prove that the fundamental ring R= γ* of R is a regular ring. Finally, we investigate the algebraic properties of M(R), the regular hyperideal of R, generated by all elements of R such that its generated hyperideal is regular. [ABSTRACT FROM AUTHOR]

Response surface methodology involving Box–Behnken design was used to evaluate the effects of three operating variables: pH, initial concentration of phosphorus, and adsorbent dosage on biosorption of phosphorus by modified Lemna minor by lab-scale batch study. Analysis of variance (ANOVA) showed pH, initial phosphorus concentration, interaction of phosphorus and adsorbent dose and the second-order effect of pH have values of “Prob. > F” less than 0.0500 indicating that model terms are significant for the biosorption of phosphorus. Optimum operational conditions for maximizing phosphorus biosorption were achieved at pH 4.8, initial phosphorus concentration of 19 mg/L and adsorbent dosage of 5.15 g/L. Under optimal value of parameters, high biosorption (89.2%) was obtained for phosphorus. Langmuir with 0.99 consistencies fitted better than Temkin, or Freundlich models. The maximum adsorption capacity of phosphorus was determined as 3.6 mg/g. Pseudo-second-order kinetic model exhibited the highest correlation with data. Results suggest that the modified L. minor has potential for biosorption as a low-cost and effective absorbent for phosphorus removal from aqueous solution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of anti fuzzy filter and study the $$\mathcal{N }$$ -subalgebra(filter) of $$CI$$ -algebra $$X$$ . We prove that every anti fuzzy filter of $$BE$$ -algebra is an anti fuzzy subalgebra, but it is not valid in $$CI$$ -algebra. Finally, the notion of fuzzy translations and fuzzy extension of anti fuzzy filter in $$CI$$ -algebras are introduced. We show that every anti fuzzy filter can be as an anti fuzzy extension, but converse may not be true in general. [ABSTRACT FROM AUTHOR]

In this paper we develop the notion of Jacobson radical to fuzzy hyperrings and studies its basic properties. In this regards, we investigate some results and definitions related to fuzzy hyperideals of fuzzy hyperrings. Then we generalize the classical case of Jacobson radical rings and ideals to fuzzy case of Jacobson radical of hyperrings and hyperideals. We will proceed focuses on the relationships of between them and studies their properties. Also, we prove a fuzzy hyperring R is semisimple if and only if it is a artinian fuzzy hyperring and Jl(R) = {0} and R be a left artinian fuzzy hyperring. Also, it is proved that R is semisimple if and only if J(R) = 0. In particular, it is shown that R/J(R) is semisimple. Also, it is prove ff R is a left artinian fuzzy hyperring, then its radical J(R) is the unique largest nilpotent left, right, or two-sided fuzzy hyperideal in R and it is shown that, if R is a fuzzy hyperring with J = J(R). Finally, it is proved R is left artinian if and only if R it is left noetherian, J is nilpotent, and R/J is semisimple. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets. [ABSTRACT FROM AUTHOR]