Lectures on the Principles of Universal Algebra

Lectures on Universal Algebra

1 Algebras In this first section we will consider some common features of familiar algebraic structures such as groups, rings, lattices, and boolean algebras to arrive at a definition of a general algebraic structure. Recall that a group G consists of a nonempty set G, along with a binary operation · : G → G, a unary operation −1 : G → G, and a constant 1 G such that • x · (y · z) = (x · y) · z...

Lectures on Commutative Algebra

Lectures on Applied Algebra

Some motivation: In this age of computers, algebra may have replaced calculus (analysis) as the most important part of mathematics. For example: 1) Error correcting codes are built into the CD player and the computer. Who do you call to correct errors? The algebraist, that’s who! 2) Digital signal processing (such as that involved in medical scanners, weather prediction, the search for oil) is ...

Notes on Universal Algebra

These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to “String Topology” and cacti are announced in Section 2.7.

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...