Lectures on injective modules and quotient rings
From MaRDI portal
Publication:2528396
DOI10.1007/BFb0074319zbMath0162.05002OpenAlexW569138506MaRDI QIDQ2528396
Publication date: 1967
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bfb0074319
semiprime ringsinjective modulesquasi-injective modulesassociative ringsmaximal ring of quotientsGoldie theoremFaith-Utumi theoremgeneralized rings of quotients
Injective modules, self-injective associative rings (16D50) Prime and semiprime associative rings (16N60) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)
Related Items
Cofinitely projective modules. II ⋮ Unnamed Item ⋮ Qi-filters and tight modules ⋮ Representation of rings with faithful polyform modules ⋮ Non-self-injective injective hulls with compatible multiplication. ⋮ Row rank and the structure of matrix subrings ⋮ Unnamed Item ⋮ Right complement bounded semiprime rings ⋮ Modules whose proper submodules are finitely generated ⋮ Artinian rings with restricted primeness conditions ⋮ Simple quotient rings of group algebras ⋮ Monomial conditions on prime rings ⋮ The quotient category of a Morita context ⋮ Self-injectivity of semigroup algebras ⋮ Fully Idempotent Rings Have Regular Centroids ⋮ Dominant modules and finite localizations ⋮ Zerlegungen von Moduln und Injektive über Ringoiden ⋮ On the matrix wreath product of algebras ⋮ Rings with quasi-injective ideals ⋮ The Structure of Rings with Faithful Nonsingular Modules ⋮ On Some Classes of Module Hulls ⋮ Right ideals and derivations on multilinear polynomials ⋮ Weakly regular and self-injective Leavitt path algebras over arbitrary graphs. ⋮ Large rings of matrices contain full rows ⋮ Semiprime rings with bounded indices of nilpotent elements ⋮ Simple self-injective rings ⋮ Prime rings with hypercommuting derivations on a Lie ideal ⋮ Modules with cyclic support ⋮ On quasi-injectivity and von Neumann regularity ⋮ Orders of direct products of simple Artinian rings ⋮ Two-sided annihilator condition with generalized derivations on multilinear polynomials ⋮ Non-Archimedean group algebras with Baer reductions ⋮ Algebras of right ample semigroups ⋮ Smooth noetherian modules ⋮ Differential identities with automorphisms and antiautomorphisms. I ⋮ Corational extensions and pseudo-projective modules ⋮ Finitely Embedded Commutative Rings ⋮ PROPERTIES OF INJECTIVE HULLS OF A RING HAVING A COMPATIBLE RING STRUCTURE ⋮ Injectivity of certain classes of modules ⋮ Nonsingular Noetherian rings of exponent 2 ⋮ Sur un problème de C. Faith ⋮ Anneaux bireguliers auto-injectifs à droite ⋮ Sur les anneaux tels que tout produit de copies d'un module quasi- injectif soit un module quasi-injectif ⋮ Serial rings and finitely presented modules ⋮ On hereditary rings and Boyle's conjecture ⋮ Idealizers in rings ⋮ Endoprojective dimension of modules ⋮ Localization at epimorphisms and quasi-injectives ⋮ On embedding torsion free modules into free modules ⋮ Dedekind Finite Rings and a Theorem of Kaplansky ⋮ Cocritically nice rings and boyle' conjecture ⋮ Injective hulls with distinct ring structures. ⋮ Endomorphism rings and lattice isomorphisms ⋮ A Subdirect Decomposition of Semiprime Rings and its Application to Maximal Quotient Rings ⋮ The hulls of semiprime rings ⋮ On dominant modules and dominant rings ⋮ S-sets and semigroups of quotients ⋮ Rings with dcc on essential left ideals ⋮ Ring geometries, two-weight codes, and strongly regular graphs ⋮ Regular Self-Injective Rings With a Polynomial Identity ⋮ The Row Rank of a Subring of a Matrix Ring ⋮ A generalization of quasi-Frobenius rings ⋮ Direct-sum representations of injective modules ⋮ On splitting of module categories ⋮ Some conditions on commutative semiprime rings ⋮ Ringerweiterung und lokalisation ⋮ A Singular Primitive Ring ⋮ Existence of ultracomplete immediate extensions for normed modules ⋮ Rings for which every cyclic module is quasi-projective ⋮ Prime ideals in regular self-injective rings. II ⋮ Rings having one-sided ideals satisfying a polynomial identity ⋮ Localization and Artinian quotient rings ⋮ Regular rings and Baer rings ⋮ Double centralizers and dominant dimensions ⋮ Quotient rings ⋮ Prime rings having one-sided ideal with polynomial identity coincide with special Johnson rings ⋮ Correspondence theorems for modules and their endomorphism rings ⋮ On twisted polynomial rings ⋮ Embedding nonsingular modules in free modules ⋮ Anneau associé à une somme directe infinie de modules quasi- injectifs. (The associative ring of an infinite direct sum of quasi- injective modules) ⋮ Essential subdirect sum decompositions of extension rings ⋮ Modules whose distinct submodules are not isomorphic ⋮ Interdirekte Summen von Moduln. (Indirect sums of modules) ⋮ The ring of endomorphisms of a finite dimensional module ⋮ Quelques remarques sur la dimension homologique des anneaux. Éléments réguliers ⋮ Finiteness in projective ideals ⋮ On rings whose simple modules are injective ⋮ Gpis Having Coefficients in Utumi Quotient Rings ⋮ On Some Rings Whose Modules Have Maximal Submodules ⋮ Weakly primitive rings ⋮ Cotorsion modules and relative pure-injectivity ⋮ Strictly invariant submodules ⋮ Quotient rings of semiprime rings with bounded index ⋮ Right-Left Symmetry of Right Nonsingular Right Max-Min CS Prime Rings ⋮ Simple regular rings and rank functions ⋮ On self-injective semigroup rings ⋮ Strongly Prime Rings ⋮ When is the Maximal Ring of Quotients Projective? ⋮ Triangular Representations of Splitting Rings ⋮ Actions of Generalized Derivations on Multilinear Polynomials in Prime Rings ⋮ On ⊕-δss-supplemented modules ⋮ Homological properties of the ring of differential polynomials ⋮ Non-local rings whose ideals are all quasi-injective ⋮ A note on locally uniform rings and modules ⋮ On potent rings, I ⋮ Generalized Quotient Rings ⋮ Right orders in full linear rings ⋮ Some dual properties on modules ⋮ On (von Neumann) regular rings ⋮ A note on cogenerators in the category of modules ⋮ Rings whose singular ideals are nil ⋮ Twisted group rings and a problem of Faith ⋮ On a generalisation of self-injective von Neumann regular rings ⋮ Simple self-injective rings need not be artinian ⋮ Die F<scp>RATTINI</scp>schen Unterstrukturen in Ringen ohne Einselement ⋮ On a Finite Dimensional Quasi-Simple Module ⋮ When is every module with essential socle a direct sum of automorphism-invariant modules? ⋮ Quotient Full Linear Rings ⋮ Balanced Rings and a Problem of Thrall ⋮ Orders in Self-Injective Cogenerator Rings ⋮ Factor Rings and Splitting Ideals of Self-Injective, CS and Baer Rings ⋮ Unnamed Item ⋮ Quotient Sheaves and Valuation Rings ⋮ On Simple Injective Rings ⋮ Quotient Rings of Endomorphism Rings of Modules with Zero Singular Submodule ⋮ Symmetric Utumi quotient rings of Ore extensions by skew derivations ⋮ Lattice-Ordered Injective Hulls ⋮ Nonsingular retractable modules and their endomorphism rings ⋮ Left Annihilators Characterized by GPIS ⋮ Endomorphism rings of torsionless modules ⋮ T-quasi continuous modules ⋮ When every endomorphism of a Σ-injective module is a sum of two commuting automorphisms ⋮ A Cohen-type theorem for w-Artinian modules ⋮ Anneaux réguliers auto-injectifs à droite ⋮ A note on regular modules ⋮ On rings with quasi-injective cyclic modules