Γ-超半群的若干研究
发布时间：2018-12-13 09:03
【摘要】：在半群代数理论中,理想在研究半群性质和刻画半群内部结构中占据重要地位.类比理想对半群的刻画方式,本文引入Γ-超半群的(m,n)拟超理想、(m,n)超理想等概念,并用它们研究Γ-超半群的性质.于此同时,提出Γ-超序半群的拟超理想、正则Γ-超序半群等概念,并给出正则Γ-超序半群用它的拟超理想刻画的方法.在第三部分中,引入Γ-超半群的(m,n)拟超理想、m-左超理想和n-右超理想的概念,给出Γ-超半群任何一个非空子集生成的(m,n)拟超理想的表示.证明任何(m,n)拟超理想可以分解为一个m-左超理想和一个n-右超理想的交,同时证明Γ-超半群的一个(m,n)拟超理想是极小的当且仅当它是某个极小m-左超理想和某个极小n-右超理想的交.最后给出(m,n)拟单超Γ-超半群的刻画.在第四部分中,引入Γ-超半群的(m,n)超理想的概念,给出Γ-超半群的(m,n)超理想的刻画和任何一个非空子集生成的(m,n)超理想的表示,并利用(m,n)超理想给出(m,n)单Γ-超半群和(m,n)正则Γ-超半群的刻画.作为本章结果的应用,当Γ只有一个元素且超运算是一般的二元运算时,半群的(m,n)理想以及利用(m,n)理想对正则半群的刻画可以相应得出.在第五部分中,作为Γ-序半群拟理想概念的推广,引入Γ-超序半群的拟超理想的概念,给出正则Γ-超序半群用其拟超理想刻画的方法,得到正则Γ-超序半群的所有拟超理想的集合Qs,关于运算“or”(对(?) X,Y∈Qs有X oΓ Y=(XΓY])构成一个正则Γ-半群,最后分别给出正则Γ-半群(QS,oΓ)是带、左正则带和半格时的内部结构.
[Abstract]:In the theory of semigroup algebra, ideals play an important role in studying the properties of Semigroups and characterizing the internal structures of Semigroups. Analogous to the characterization of Semigroups by ideals, this paper introduces the concepts of (mtn) quasi superideals and (mtn) superideals of 螕 -hypersemigroups, and uses them to study the properties of 螕 -hypersemigroups. At the same time, the concepts of quasi-superideal and regular 螕 -supersequence semigroup of 螕 -supersequence semigroup are proposed, and the method of characterizing regular 螕 -supersorded semigroup by its quasi superideal is given. In the third part, we introduce the concepts of (mn) quasi superideal, mleft superideal and n-right superideal of 螕 -hypersemigroup, and give the representation of (mn) quasi-superideal generated by any nonempty subset of 螕 -hypersemigroup. It is proved that any (mn) quasi superideal can be decomposed into the intersection of an m-left superideal and a n-right superideal, and that a 螕 -hypersemigroup (m, N) Quasi-superideal is minimal if and only if it is the intersection of a minimal m-left superideal and a minimal n-right superideal. Finally, the characterizations of (mtn) quasi-simple 螕 -hypersemigroup are given. In the fourth part, we introduce the concept of (mtn) superideal of 螕 -hypersemigroup, and give the characterization of (mn) superideal of 螕 -hypersemigroup and the representation of (mn) superideal generated by any nonempty subset. N) the characterizations of (mtn) simple 螕 -hypersemigroups and (mdrn) regular 螕 -hypersemigroups are given. As an application of the results in this chapter, when 螕 has only one element and the hyper-operation is a general binary operation, the (mn) ideals of Semigroups and the characterizations of regular Semigroups by using (mtn) ideals can be obtained accordingly. In the fifth part, as a generalization of the concept of quasi-ideal of 螕 -ordered semigroup, the concept of quasi-superideal of 螕 -ordered semigroup is introduced, and the method of characterizing regular 螕 -superscript semigroup by its quasi-superideal is given. We obtain the set Qs, of all quasi-superideals of regular 螕 -superordered Semigroups on the operation "or" (for (?) XY 鈭，
本文编号：2376285
[Abstract]:In the theory of semigroup algebra, ideals play an important role in studying the properties of Semigroups and characterizing the internal structures of Semigroups. Analogous to the characterization of Semigroups by ideals, this paper introduces the concepts of (mtn) quasi superideals and (mtn) superideals of 螕 -hypersemigroups, and uses them to study the properties of 螕 -hypersemigroups. At the same time, the concepts of quasi-superideal and regular 螕 -supersequence semigroup of 螕 -supersequence semigroup are proposed, and the method of characterizing regular 螕 -supersorded semigroup by its quasi superideal is given. In the third part, we introduce the concepts of (mn) quasi superideal, mleft superideal and n-right superideal of 螕 -hypersemigroup, and give the representation of (mn) quasi-superideal generated by any nonempty subset of 螕 -hypersemigroup. It is proved that any (mn) quasi superideal can be decomposed into the intersection of an m-left superideal and a n-right superideal, and that a 螕 -hypersemigroup (m, N) Quasi-superideal is minimal if and only if it is the intersection of a minimal m-left superideal and a minimal n-right superideal. Finally, the characterizations of (mtn) quasi-simple 螕 -hypersemigroup are given. In the fourth part, we introduce the concept of (mtn) superideal of 螕 -hypersemigroup, and give the characterization of (mn) superideal of 螕 -hypersemigroup and the representation of (mn) superideal generated by any nonempty subset. N) the characterizations of (mtn) simple 螕 -hypersemigroups and (mdrn) regular 螕 -hypersemigroups are given. As an application of the results in this chapter, when 螕 has only one element and the hyper-operation is a general binary operation, the (mn) ideals of Semigroups and the characterizations of regular Semigroups by using (mtn) ideals can be obtained accordingly. In the fifth part, as a generalization of the concept of quasi-ideal of 螕 -ordered semigroup, the concept of quasi-superideal of 螕 -ordered semigroup is introduced, and the method of characterizing regular 螕 -superscript semigroup by its quasi-superideal is given. We obtain the set Qs, of all quasi-superideals of regular 螕 -superordered Semigroups on the operation "or" (for (?) XY 鈭，
本文编号：2376285
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