# H. Saadat's scientific contributions

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## Publications (3)

The following results for the space X of the fuzzy prime spectrum of a given bounded implicative BCK-algebra Y are proved: 1. The topological space X is Lindelöf and disconnected. 2. If Y is an integral domain, then X is irreducible.

In this paper some properties of the uniformity topology on a BCI-algebras are discussed.

First we show that the cosets of a fuzzy idea µ in a BCK-algebra X form another BCK-algebra X µ (called the fuzzy quotient BCK-algebra of X by µ). Also we show that X µ is a fuzzy partition of X, and prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BC...

## Citations

... It is now natural to consider similar style of generalizations of the existing fuzzy subsystems of other algebraic structures. For this reason, we decided to define and investigated these notions on hoop algebras, which we studied [20][21][22][23] for sources of inspiration and ideas for this paper. Definition 1. [24] Let (H, , →, 1) be a bounded hoop. ...

... [37,Theorems 4.3,4.4,4.10,4.11,4.12,4.14,Corollary 4.4], [29,Proposition 4 Filter (BL-algebras) [14,15,21] Extreme fuzzy filter (BL-algebras) [37] Filter (MV-algebras) [3] Riesz ideal (effect algebras) [29] Weakly algebraic ideal (effect algebras) [23] Filter (EQ-algebras) [34] Regular ideal (BCC-algebras) [25] BCC-ideal (BCC-algebras) [2] Filter (residuated lattices) [12,13] Fuzzy filter (residuated lattices) [11] Filter (BE-algebras) [24,27] Ideal (difference algebra) [4] Deductive system (Hilbert algebra) [5,26] d * -ideal (d-algebra) [6] Ideal (subtraction algebras) [1] Ideal (BCI-algebras) [28,35] Filter (fuzzy implication algebras) [30] Implicative filter (positive implication algebras) [19] Dual ideal (BCK-algebras) [20] Hyper K-ideal (hyper K-algebras) [7] Extreme fuzzy filter (equality algebras) [36] Very true filter (very true equality algebras) [33] S-reflexive hyper MV-filter (hyper MV-algebras) [10] There are many different kinds of congruence relations on algebraic systems. For example, read about the theory of filters on residuated structures in [8] and [32]. ...