Geodesic
Some Properties Associated with Adequate Transversals
Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 487-497

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In this paper, another relationship between the quasi-ideal adequate transversals of an abundant semigroup is given. We introduce the concept of a weakly multiplicative adequate transversal and the classic result that an adequate transversal is multiplicative if and only if it is weakly multiplicative and a quasi-ideal is obtained. Also, we give two equivalent conditions for an adequate transversal to be weakly multiplicative. We then consider the case when $I$ and $\Lambda $ (defined below) are bands. This is analogous to the inverse transversal if the regularity condition is adjoined.
DOI : 10.4153/CMB-2011-015-8
Mots-clés : 20M10, abundant semigroup, adequate transversal, Green's ∗-relations, quasi-ideal 
Kong, Xiangjun. Some Properties Associated with Adequate Transversals. Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 487-497. doi: 10.4153/CMB-2011-015-8
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     author = {Kong, Xiangjun},
     title = {Some {Properties} {Associated} with {Adequate} {Transversals}},
     journal = {Canadian mathematical bulletin},
     pages = {487--497},
     year = {2011},
     volume = {54},
     number = {3},
     doi = {10.4153/CMB-2011-015-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-015-8/}
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