caa a22 4500 445345314 CHVBK 20180317142827.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00233-011-9309-7 doi (NATIONALLICENCE)springer-10.1007/s00233-011-9309-7 The product of quasi-ideal adequate transversals of an abundant semigroup [Elektronische Daten] [Xiangjun Kong, Pei Wang] An inverse transversal of a regular semigroup S is an inverse subsemigroup that contains precisely one inverse of each element ofS. This concept was first introduced by Blyth and McFadden and generalized to an adequate transversal in the abundant case by El-Qallali. In this paper we show that the product of any two quasi-ideal adequate transversals of an abundant semigroup S which satisfy the regularity condition is a quasi-ideal adequate transversal of S. Furthermore, all adequate transversals of S form a rectangular band. Springer Science+Business Media, LLC, 2011 Regular semigroup nationallicence Abundant semigroup nationallicence Inverse transversal nationallicence Adequate transversal nationallicence Quasi-ideal nationallicence Kong Xiangjun School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, Shandong, People's Republic of China aut Wang Pei School of Computer Science, Qufu Normal University, 273165, Qufu, Shandong, People's Republic of China aut Semigroup Forum Springer-Verlag 83/2(2011-10-01), 304-312 0037-1912 83:2<304 2011 83 233 https://doi.org/10.1007/s00233-011-9309-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9309-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kong Xiangjun School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, Shandong, People's Republic of China aut NATIONALLICENCE 700 1- Wang Pei School of Computer Science, Qufu Normal University, 273165, Qufu, Shandong, People's Republic of China aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/2(2011-10-01), 304-312 0037-1912 83:2<304 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer