h.s. kim

Using the fuzzy points, the concept of (∈, ∈)-fuzzy filters of equality algebras is introduced, and related properties are investigated. Characterizations of (∈, ∈)-fuzzy filters are explored, and the conditions under which ∈t-set, qt-set, and positive set can be filters are investigated.

In this paper, we discuss some iterations and apply it to $d/BCK$-algebras and semigroups. Given a $BCK$-algebra $(X,*, 0)$, we construct an edge $d$-algebra by using the notion of iterations.

Plasma cell neoplasm is a group of disorders involving mature B-cells that results in excessive production of specific monoclonal heavy-chain immunoglobulins. Plasma cell neoplasm can present in different clinical forms. 

 An elderly female presented with long-standing nasal congestion and was diagnosed with nasal plasmacytoma. After a complete checkup, including 2-[18F] fluorodeoxyglucose (FDG) positron emission tomography (PET)/ computed tomography (CT), a diagnosis of extramedullary nasal plasmacytoma with synchronous multiple myeloma was concluded. Herein, we report a single case of a patient with extramedullary nasal plasmacytoma and synchronous multiple myeloma, including its clinical and imaging findings. 

Multiple myeloma shows generally poor prognosis. Conversely, the prognosis of extramedullary plasmacytoma is good, and recurrence, metastasis, and transformation into multiple myeloma are rare. It is important to distinguish solitary plasmacytoma from other plasma cell diseases to choose the best treatment. A systemic understanding of the clinical and imaging features of extramedullary plasmacytoma and multiple myeloma are may help clinical and imaging doctors correctly diagnose the disease.

In this paper, we introduce the notion of a ringoid, and we obtain left distributive ringoids over a field which are not rings. We introduce several different types of ringoids, and also we discuss on (r, s)-ringoids. Moreover, we discuss geometric observations of the parallelism of vectors in several ringoids.

In this paper, we introduce the notion of a block commutativity in several groupoids, and show that the class of block commutative groupoids and the class of d/BCK-algebras are Smarandache disjoint. The block commutativity in linear/quadratic groupoids is investigated, and we prove that every group is a normal groupoid. Moreover, we discuss block n-commutative groupoids and block ranks.