semilocal ringuniserial moduleprojective modulepure-projective moduleglobal dimensionWe investigate the module theory of a certain class of semilocal rings connected with nearly simple uniserial domains. For instance, we classify finitely presented and pure-projective modules over these rings and calculate...
Projective modules over rings with many units Let be a commutative ring. Assume that every polynomial whose values generate the unit ideal actually takes on an invertible value. Then projective -module... BR Mcdonald,WC Waterhouse - 《Proceedings of the American Mathematical Society》 被引量: 37...
Projective modules over polynomial rings. Invent Math 36, 167–171 (1976). https://doi.org/10.1007/BF01390008 Download citation Received01 March 1976 Issue DateDecember 1976 DOIhttps://doi.org/10.1007/BF01390008 Keywords Vector Bundle Local Ring Polynomial Ring Projective Module Noetherian Ring ...
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,. . . ...
A separative ring is one whose finitely generated projective modules satisfy the propertyA⊕A⋟A⊕B⋟B⊕B⇒A⋟B. This condition is shown to provide a key to a number of outstanding cancellation problems for finitely generated projective modules over exchange rings. It is shown that the ...
The fundamental theorem of the homomorphism ring can be applied to the non-associative rings. By a little modification, we can find that is isomorphic to . Furthermore, we define a module over a non-associative ring and investigate ... IK Waliyanti,IE Wijayanti,MF Rosyid - 《Mathematics &...
This paper gives the structure of finitely cogenerated sub-projective modules and the structure of sub-projective modules over a semilocal ring.The characterizations of semisimple and semilocal rings via sub-projectivity are also given.关键词: projective radical sub-projective module semilocal ring 被...
local splitting properties of endomorphism rings of projective modules Let B be a discrete Hodge algebra over a Noetherian d-dimensional ring A and P a projective module over B. Write B as R/I, where I is generated by monomial... CL Sang 被引量: 0发表: 2017年 PROJECTIVE PROPERTIES OF ...
statements are equivalent for a commutative Noetherian domain R: (a) R is a one-dimensional Gorenstein ring; (b) R/Ra is a self-injective ring for all nonzero a in R; (c) the R-module R⊕R is self-c-injective; (d) every finitely generated projective R-module is self-c-injective...
On Modules of Finite Projective Dimension over Complete Intersections Recently Avramov and Miller proved that over a local complete intersection ring (R,m,k) in characteristic $p>0$, a finitely generated module... SP Dutta - 《Proceedings of the American Mathematical Society》 ...