Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.
It's the end of Christianity as we know it. But it's not a catastrophe-it's an opportunity. Thousands are walking away from the church. Christians are grappling with their faith. And both believers and nonbelievers wondering-what's coming next? Fearless and provocative, spiritual trailblazer Christian Piatt offers a roadmap to the future of faith with an unflinching examination of the church today. What's left? Pairing the best "virtues" and worst "scandals" of Christianity, Piatt invites us to abandon institutional religion for deeper, truer faith. Can we fix it? Guided by the biggest historical, religious, and pop-cultural pioneers of the post Christian era, he demonstrates how to save the best of what Christianity has to offer-and how to rediscover and reinvent the rest. Do we care? There's plenty of good left in Christianity-if we dare to be as scandalously graceful and loving as Jesus Himself. Bold and insightful, Postchristian dares Christians to break out of the box and invites outsiders into the fold as we revolutionize faith for a postmodern world.
Have you ever had a burning question that seemed off limits or inappropriate to ask about Christianity, the Bible, or Jesus? You Can’t Ask That! gathers 50 of the most provocative, challenging, or otherwise taboo questions that many of us have wondered about but few have actually asked. Edited by Christian Piatt, who once had a bible thrown at his head for asking too many questions during a Sunday school class, this collection considers nothing off limits and takes the hard questions seriously. Responses from theology professors, pastors, lay leaders, and other progressive Christians range from the personal to the profound and from sarcastic to deeply touching. By offering multiple perspectives to those banned questions, readers can craft their own answers. Better yet, they’ll understand that questioning faith is not taboo; it’s the foundation of a strong and growing faith.
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.
This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.
With its focus on drugs so recently introduced that they have yet to be found in any other textbooks or general references, the information and insight found here makes this a genuinely unique handbook and reference. Following the successful approach of the previous volumes in the series, inventors and primary developers of successful drugs from both industry and academia tell the story of the drug's discovery and describe the sometimes twisted route from the first drug candidate molecule to the final marketed drug. The 11 case studies selected describe recent drugs ranging across many therapeutic fields and provide a representative cross-section of present-day drug developments. Backed by plenty of data and chemical information, the insight and experience of today's top drug creators makes this one of the most useful training manuals that a junior medicinal chemist may hope to find. The International Union of Pure and Applied Chemistry has endorsed and sponsored this project because of its high educational merit.
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