Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finitely generated R-module P is projective iff there is an R-module Q with P @ Q S Rn for some n. Remarkably enough there do exist nonfree projective modules. Even there are nonfree P such that P @ Rm S Rn for some m and n. Modules P having the latter property are called stably free. On the other hand there are many rings, all of whose projective modules are free, e. g. local rings and principal ideal domains. (A commutative ring is called local iff it has exactly one maximal ideal. ) For two decades it was a challenging problem whether every projective module over the polynomial ring k[X1,. . .

Cosmopolitanism is the idea of humanity as a single community or polis. Beyond particularities, all human beings (and in some versions of cosmopolitanism certain non-humans) are part of a community, and have responsibilities, rights and the power to decide on a common future. Ideas of cosmopolitan vary from the purely moral to cultural, social, legal, institutional, political, educational and economic cosmopolitanism, or combine some or all of these facets. All of these different perspectives try to establish the basis necessary to create a true cosmopolitanism. This book provides an introduction to the ideality and reality of cosmopolitanism, presenting it “in genesis” and giving a point of departure to students and readers of cosmopolitanism from which to analyse its various contemporary versions and proposals, providing an additional tool for their thinking and judgments in the face of a huge amount of literature today. It also offers a sense of emergency to those matters, requiring a prompt legal, political and economic response, for the continuing existence of the planet and for cosmopolitanism to continue as a viable proposal for humanity. As such, this volume will, ultimately, provoke the reader into a new spirit and action, that of cosmopolitanism.

Brown Landone was one of the first teachers of the scientific understanding of material and immaterial achievements in life. For his first 13 years he lived the usual routine of an invalid. Then his life changed dramatically. Although virtually helpless by many medical accounts, he was able to carry a heavy metal crate down five flights of stairs when he was left alone and a house fire broke out. Afterwards, young Landone knew that his subconscious had made it happen somehow. He figured that if he could do it on a subconscious level, he could certainly do it on a conscious level. This book is an important guide for those who have decided to use the immense power of their Subconscious and make a positive and decisive change in their lives.

This book sets out the case for a cosmopolitan approach to contemporary global politics. It presents a systematic theory of cosmopolitanism, explicating its core principles and justifications, and examines the role many of these principles have played in the development of global politics, such as framing the human rights regime. The framework is then used to address some of the most pressing issues of our time: the crisis of financial markets, climate change and the fallout from the wars in Afghanistan and Iraq. In each case, Held argues that realistic politics is exhausted, and that cosmopolitanism is the new realism. See also Garrett Wallace Brown and David Held's The Cosmopolitanism Reader.

"Is geography one, or is it several subjects? More precisely, are physical and political geography two stages of one investigation, or are they separate subjects to be studied by different methods, the one an appendix of geology, the other of history? " --Halford Mackinder in The Scope and Methods of Geography, 1887 The Scope and Methods of Geography was published by Halford Mackinder in 1887 in the "New Monthly Series of the Royal Geographical Society." It was a manifesto for the New Geography, in which he viewed physical geography and human geography as a single discipline. This publication represented the beginning of an illustrious career as an English geographer and academic.