In this paper,first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism.Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner h...In this paper,first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism.Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4.Moreover,we propose a hyperfield of order 4 which is not as a quotient hyperfield F/G.Finally,some programs written in MATLAB which are based on obtained results compute the number of polygroups,weak polygroups and Krasner hyperfields of order4 up to isomorphism.展开更多
Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then th...Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then the m-ary hyperoperations defined on the quotient canonical(m,n)-ary hypermodule[M:N^(*)]are m-ary operations and the relation N^(*)is a strongly regular relation.Further,in this case,it is shown that the scalar hyperoperation is just an operation.展开更多
In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasne...In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.展开更多
文摘In this paper,first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism.Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4.Moreover,we propose a hyperfield of order 4 which is not as a quotient hyperfield F/G.Finally,some programs written in MATLAB which are based on obtained results compute the number of polygroups,weak polygroups and Krasner hyperfields of order4 up to isomorphism.
文摘Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then the m-ary hyperoperations defined on the quotient canonical(m,n)-ary hypermodule[M:N^(*)]are m-ary operations and the relation N^(*)is a strongly regular relation.Further,in this case,it is shown that the scalar hyperoperation is just an operation.
基金supported by a Grant of National Natural Science Foundation of China(Grant Nos.11461025and 11561023)
文摘In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.
