The divisibility theory of commutative rings
is a fundamental and persisting topic in mathematics that entails two main aspects: determining irreducibility and finding a factorization of the reducible elements in the ring.
He walks readers who have a reasonable acquaintance with the more elementary facts concerning commutative rings
and modules through most of the known results on formal groups, and applications that do not require too much extra apparatus.
Smith defined weakly prime ideals in commutative rings
, an ideal P of a ring R is weakly prime if 0 [not equal to] ab [member of] P implies a [member of] P or b [member of] P.
Chapters address group theory, commutative rings
, Galois theory, noncommutative rings, representation theory, advanced linear algebra, and homology.
For one, by building on the well-studied setting of modules over commutative rings
, we get a theory where the considerable power and development of commutative algebra can be easily brought to bear.
They also include graphs for algebraic structures like commutative semigroups, loops, communicative groupoids, and commutative rings
Chapters consider local and reduced rings, and commutative rings
in general, as well as the classification of minimal ring extensions, linear systems theory over commutative rings
, and the history and summary of asymptotic stability of associated or attached prime ideals.
The 64 papers in this collection explore field theory and polynomials, commutative rings
and algebras, matrix theory, associative rings, K-theory, group theory and generalizations, topological groups, Lie groups, and differential geometry.
Fourteen papers accepted for the December 2006 conference describe the structure of incidence rings of group automata, apply diagram categories from statistical mechanics to representation theory, and examine determinantal and Pfaffian ideals of symmetric matrices over general commutative rings
Brzezinski (University of Wales) and Wisbauer (Heinrich Heine University) develop the theory of coalgebras over commutative rings
and their comodules, and present known results on the structure of corings.
Arithmetic properties of commutative rings
Hirano, On annihilator ideals of a polynomial ring over a non commutative ring