@inbook{926841f712754b9cb0e932280d453d9c,
title = "Cross-connections in Clifford semigroups",
abstract = "An inverse Clifford semigroup (often referred to as just a Clifford semi-group) is a semilattice of groups. It is an inverse semigroup and in fact, one of the earliest studied classes of semigroups (Clifford in Ann Math 42(4):1037-1049 (1941), [6]). In this short note, we discuss various structural aspects of a Clifford semigroup from a cross-connection perspective. In particular, given a Clifford semigroup. S, we show that the semigroup.T L(S) of normal cones is isomorphic to the original semigroup. S, even when. S is not a monoid. Hence, we see that cross-connection description degenerates in Clifford semigroups. Further, we specialise the discussion to provide the description of the cross-connection structure in an arbitrary semilattice, also.",
keywords = "Clifford semigroups, Cross-connections, Inverse semigroups, Normal categories, Semilattices",
author = "\{Azeef Muhammed\}, \{P. A.\} and Preenu, \{C. S.\}",
year = "2023",
doi = "10.1007/978-981-99-6349-2\_1",
language = "English",
isbn = "9789819963485",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "3--9",
editor = "Ambily, \{A. A.\} and \{Kiran Kumar\}, \{V. B.\}",
booktitle = "Semigroups, Algebras and Operator Theory, ICSAOT 2022, CUSAT, India, March 28 - 31",
note = "International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT ; Conference date: 28-03-2022 Through 31-03-2022",
}