As a researcher trying to publish a scholarly article or book, you are typically asked by the publisher to sign a copyright transfer agreement, or contract, that describes the transference of some --or all-- of the exclusive rights that you have under copyright law in your creative work.
Author amendments --or author addenda-- are legal instruments that modify the publisher’s agreement and allow you to keep some of the rights to your publications, such as online archiving, adding a copy to your website, re-use in future publications and presentations, distribution to students for teaching purposes, etc.
If you have been asked to transfer your copyright to a publisher, know that those publishing agreements are negotiable. If you want to retain some of your rights, consider sending a copy of the University of Rochester Author's Amendment to the publisher and explaining why it is important for you to retain those rights in your own work.
More and more publishers are developing alternative contracts that allow for open access privileges, for example. Check your options before signing your rights. Talk to your librarian if you have any questions.
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