"Indexes which do not permit any two rows in the specified columns to have the same value. SQL Server checks for duplicate values when you create the index (if data already exists) and each time data is added." (Karen Paulsell et al, "Sybase SQL Server: Performance and Tuning Guide", 1996)
"Restricts duplicate values in a column." (Owen Williams, "MCSE TestPrep: SQL Server 6.5 Design and Implementation", 1998)
"An index in which no two rows are permitted to have the same index value, thus prohibiting duplicate index or key values. The system checks for duplicate key values when the index is created and checks each time data is added with an INSERT or UPDATE statement." (Microsoft Corporation, "SQL Server 7.0 System Administration Training Kit", 1999)
"An index with perfect selectivity, that is, an index with no duplicate values allowed. Standard SQL allows multiple NULLs in a unique index, since a NULL is not considered to be equal to any other value, including another NULL. Many DBMSs, however, accept only one NULL in a unique index. Some DBMSs won't allow even a single NULL." (Peter Gulutzan & Trudy Pelzer, "SQL Performance Tuning", 2002)
"A b-tree index whose keys are not duplicated." (Bob Bryla, "Oracle Database Foundations", 2004)
"This is a special index that prevents users from inserting the same value into a column (or columns) more than once." (Joseph L Jorden & Dandy Weyn, "MCTS Microsoft SQL Server 2005: Implementation and Maintenance Study Guide - Exam 70-431", 2006)
"An index that enforces uniqueness for a particular field across a single collection." (MongoDb, "Glossary", 2008)
"Sometimes created explicitly by the user, and sometimes created automatically by the database server. By guaranteeing one-and-only-one value for a given table, this structure speeds access to information and preserves data integrity." (Robert D. Schneider and Darril Gibson, "Microsoft SQL Server 2008 All-In-One Desk Reference For Dummies", 2008)
"An index in which no two rows are permitted to have the same index value, thus prohibiting duplicate index or key values." (Microsoft, "SQL Server 2012 Glossary,", 2012)
"An index that ensures that no identical key values are stored in a column or a set of columns in a table." (Sybase, "Open Server Server-Library/C Reference Manual", 2019)