Introduction: homological and commutative algebra
نویسنده
چکیده
Naive set theory is the typical background or foundation for constructing more complicated structures, in a century-old tradition. The modifier naive denotes an informal and non-axiomatic treatment, in contrast to versions of set theory specifically aimed at preventing paradoxes by limiting constructions. Part of the set theory tradition demands that any mathematical discussion be compatible with the explicit or implicit prohibitions of set theory.
منابع مشابه
Derived Category Methods in Commutative Algebra II
In our report on the first “Derived Category Methods in Commutative Algebra” workshop (2008) we wrote: “Derived category methods have proved to be very successful in ring theory, in particular in commutative algebra. Evidence is provided by [1, 8, 4, 5, 6, 7, 11, 12, 15, 16, 19, 20, 23, 24, 27], to list some work of considerable importance. Surprisingly, there is no accessible introduction or r...
متن کاملGorenstein Homological Dimensions of Commutative Rings
The classical global and weak dimensions of rings play an important role in the theory of rings and have a great impact on homological and commutative algebra. In this paper, we define and study the Gorenstein homological dimensions of commutative rings (Gorenstein projective, injective, and flat dimensions of rings) which introduce a new theory similar to the one of the classical homological d...
متن کاملComputing “Small” 1–Homological Models for Commutative Differential Graded Algebras
We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the differential structure of a small 1–homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer package in Mathematica is described for determining such models.
متن کاملComputing “Small” 1–Homological Models for Commutative Differential Graded Algebras
We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the differential structure of a small 1– homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer package in Mathematica is described for determining such models.
متن کاملHomological Dimension of Smash Product over Quasitriangular Weak Hopf Algebra
Let (H,R) be a quasitriangular weak Hopf algebra, and A a quantum commutative weak H-module algebra. We establish the relationship of homological dimensions between weak smash product algebra A#H and A under some conditions. As an application, we consider the case of twisted weak Hopf algebra. Mathematics Subject Classification (2010): 16T05
متن کاملOn Commutative Algebra and Characteristic-free Representation Theory
A description of the thread holding together commutative algebra, homological algebra and representation theory. A discussion of some of the developments in the area of determinantal ideals, Schur and Weyl modules, and their interrelationships.
متن کامل