偏序半群的偏序同态与商序同态的若干重要性质

通过偏序半群的左理想和理想化子,对偏序半群的偏序同态与商序同态的性质进行了刻画。

On Left A-Injective Rings

The main results of this paper are following theorems: (1)A left A-injective ring satisfying the ascending chain condition on right annihilator is QF ring. (2)A left A-injective ring satisfying the ascending hain condition on left annihilator is QF ring. (3)If R satisfies the following conditions: (ⅰ) r(A∩B)=r(A)+r(B), for each pair of left ils A,B;(ⅱ) rl(I)=I, for every right ideal I. Then R is semiperfect ring and has essential left s. In particular, any right CF left A-injective (or E(_RR) is projective left R-module) is QF ring

The Global Value ofMencius＇s Ideas on Moral Feeling and Reason： Reinterpreting the Feeling of Compassion From the Perspective of the Philosophy of Emotion

Amid the recent global upsurge of studies on the philosophy of emotion, a reinterpretation of traditional Confucian philosophy, especially Mencius＇s ideas on the siduan （Four Original Sources） of morality, may shed new light on the subject in comparative philosophy. This paper probes the structure of moral feeling and reason described by Mencius＇s from five perspectives： （1） In view of the relationship between feeling and reason, is it better to use the expression ＂siduan＂ or the expression ＂sixin （Four Heart-minds）＂？ （2） In view of dispositional feeling, what are the four original sources？ （3） In view of moral feeling, what are the structural order of the four sources and the corresponding procedure of reasoning of four heart-minds of Humanity？ （4） In view of positive feeling, how does moral feeling grow out of the goodness of human nature？ （5） What is the global value of Mencius＇s ideas on human moral feeling？ The author concludes that Mencius＇s thought on moral feeing has a global value and cross-cultural significance, and that Chinese wisdom is more than regional but universally applicable. The structure of moral feeling and reason that Mencius identified is in accordance with the principles ofzhiliang （grasping the two poles of the beginning and the end） and yongzhong （emloying the middle）. The principles ofzhiliang and yongzhong are true universal wisdoms of Confucianism, which should be rekindled today. From a practical point of view, ＂the Way begins from moral feelings,＂ and Confucius and Yah Hui＇s seeking the simple, virtuous life is an ideal model of emotional well-being.

The Dates of the Reign of Vakhtang Gorgasali

Georgian historiography dates the reign of King Vakhtang Gorgasali （Gorg-a-sar--＇wolf-head＇ in Persian） to the 2nd half of 5th century. The king is considered to have died in 502 in a fight with Persians. Cyril Toumanoff has expressed an opinion about the identification of Vakhtang Gorgasali with the King of Kartli Gurgen, mentioned by Procopius of Caesarea in 523. Accordingly, he believed that in case of such an identification, Vakhtang Gorgasali should have died in 527 during the big Persian invasion of Georgia. We have noticed that the author of the martyrdom of David and Constantine, who were based on the ancient chronicle （＂Dzveli Utskebani＂---Old Story） and who created his hagiographic work in the middle of 1 lth century, made a big mistake： erroneously, due to the similarity of names, he identified the sons of Georgian King Vakhtang Gorgasali Darchil and Mihrdat and the invasion of Persians in their reign with the sons of the ruler of Georgia （Kartli） Stephanoz III Mihrdat and Archil and invasions of Arabs and Marwan ibn Muhammad （Murvan Qru--＂Marwan the Deaf＇） that took place two centuries later, in the 30s of 8th century. Consequently, the author related the martyrdom on the background of Arab invasions. The fact that according to the author of the martyrdom, the sons of Vakhtang Gorgasali were in West Georgia, namely Anakopia, and fought the so-called Arabs there, makes it clear that the historical developments were taking place in the period of the Great Persian-Byzantine War of 542-562. In the title of the work it is mentioned that the invasion, during which the martyrdom of David and Constantine took place, happened in the vicinity of the death of Vakhtang Gorgasali. Thus, it becomes clear that King Vakhtang Gorgasali could not have died during the Persian-Byzantine War of 502-505 and that the Great Invasion of Persians described in the ＂Georgian Chronicles＂, in which Vakhtang Gorgasali was wounded, could only have happened in 527. The king must have died during a war between Persia and Byzantium in 527-532, more specifically in 527 when Persians invaded Georgia. Proceeding from the above, the surmise of Cyril Toumanoff regarding the death of Vakhtang Gorgasali in 527 becomes more convincing and well-grounded. Since it is known that King Vakhtang Gorgasali lived 60 years, the date of his birth can be presumed to be 466-467. This gives us an opportunity to establish a more precise date of reign ofVakhtang＇s father-Mihrdat and his grandfather-Archil. The dates of reign we have put forward for kings Mihrdat and Archil （Archil ,130-463, Mihrdat--463-473） correspond to the information of the Assyrian version of the Life of Peter the Iberian.

The Cyborg Entity in Gibson＇s Neuromancer： An Idealistic ＂Cyborg Manifesto？＂

The idea of Cyborg initiates the blurring of frontiers between traditional gender roles in the post-modem era, transforming itself into a politicized entity. William Gibson＇s Neuromancer as an early introducer of the Cyborg characters tries to dissolve the boundaries through his female characters by balancing the power quota with the help of the non-gendered entity of the Cyborg. According to Donna Haraway, there will be a dawn of new cyborg era causing a gender role reversal. The objective of this paper is to find whether such role reversal is at all possible.

A Note on AP-Injective Rings

The purpose of this paper is to study the following two questions on AP-injective rings: (1) R is a regular ring if and only if R is a left PP-ring and R is left AP-injective; (2) Let R be a right .AP-injective ring. Then R is self-injective if and only if R is weakly injective. Hence we get some new results of P-injective rings.

Double-bosonization and Majid's conjecture(IV): Type-crossings from A to BCD

Both in Majid's double-bosonization theory and in Rosso's quantum shuffle theory, the rankinductive and type-crossing construction for U_q(g)'s is still a remaining open question. In this paper, working in Majid's framework, based on the generalized double-bosonization theorem we proved before, we further describe explicitly the type-crossing construction of U_q(g)'s for(BCD)_n series directly from type An-1via adding a pair of dual braided groups determined by a pair of(R, R′)-matrices of type A derived from the respective suitably chosen representations. Combining with our results of the first three papers of this series, this solves Majid's conjecture, i.e., any quantum group U_q(g) associated to a simple Lie algebra g can be grown out of U_q(sl_2)recursively by a series of suitably chosen double-bosonization procedures.