【摘要】：在半群代數(shù)理論中,理想在研究半群性質(zhì)和刻畫半群內(nèi)部結(jié)構(gòu)中占據(jù)重要地位.類比理想對(duì)半群的刻畫方式,本文引入Γ-超半群的(m,n)擬超理想、(m,n)超理想等概念,并用它們研究Γ-超半群的性質(zhì).于此同時(shí),提出Γ-超序半群的擬超理想、正則Γ-超序半群等概念,并給出正則Γ-超序半群用它的擬超理想刻畫的方法.在第三部分中,引入Γ-超半群的(m,n)擬超理想、m-左超理想和n-右超理想的概念,給出Γ-超半群任何一個(gè)非空子集生成的(m,n)擬超理想的表示.證明任何(m,n)擬超理想可以分解為一個(gè)m-左超理想和一個(gè)n-右超理想的交,同時(shí)證明Γ-超半群的一個(gè)(m,n)擬超理想是極小的當(dāng)且僅當(dāng)它是某個(gè)極小m-左超理想和某個(gè)極小n-右超理想的交.最后給出(m,n)擬單超Γ-超半群的刻畫.在第四部分中,引入Γ-超半群的(m,n)超理想的概念,給出Γ-超半群的(m,n)超理想的刻畫和任何一個(gè)非空子集生成的(m,n)超理想的表示,并利用(m,n)超理想給出(m,n)單Γ-超半群和(m,n)正則Γ-超半群的刻畫.作為本章結(jié)果的應(yīng)用,當(dāng)Γ只有一個(gè)元素且超運(yùn)算是一般的二元運(yùn)算時(shí),半群的(m,n)理想以及利用(m,n)理想對(duì)正則半群的刻畫可以相應(yīng)得出.在第五部分中,作為Γ-序半群擬理想概念的推廣,引入Γ-超序半群的擬超理想的概念,給出正則Γ-超序半群用其擬超理想刻畫的方法,得到正則Γ-超序半群的所有擬超理想的集合Qs,關(guān)于運(yùn)算“or”(對(duì)(?) X,Y∈Qs有X oΓ Y=(XΓY])構(gòu)成一個(gè)正則Γ-半群,最后分別給出正則Γ-半群(QS,oΓ)是帶、左正則帶和半格時(shí)的內(nèi)部結(jié)構(gòu).
[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，

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