We study the class of ADS rings and modules introduced by Fuchs. We give some connections between... more We study the class of ADS rings and modules introduced by Fuchs. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R is ADS as a right R-module must be either right self-injective or indecomposable as a right R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.
Leavitt path algebras of Cayley graphs arising from cyclic groups by G. Abrams and B. Schoonmaker... more Leavitt path algebras of Cayley graphs arising from cyclic groups by G. Abrams and B. Schoonmaker Characterizations of almost injective modules by A. Alahmadi, S. K. Jain, and S. Singh Automorphism-invariant modules by P. A. Guil Asensio and A. K. Srivastava Distributive algebras, isoclinism, and invariant probabilities by S. M. Buckley Ideals of the enveloping algebra $U(sl_3)$ by S. Catoiu On second submodules by S. Ceken and M. Alkan Open problems in coding theory by S. T. Dougherty, J.-L. Kim, and P. Sole Foundations of algebraic coding theory by S. T. Dougherty Counting $\mathbb{Z}_2\mathbb{Z}_4$-additive codes by S. T. Dougherty and E. Salturk From endomorphism rings to some noteworthy ideals in categories of modules by A. Facchini Lie and Jordan properties in group algebras by E. G. Goodaire and C. P. Milies Rad-projective $\delta$-covers by Y. Ibrahim and M. Yousif On lattices of annihilators by M. Jastrzebska and J. Krempa Clean elements in polynomial rings by P. Kanwar, A....
Separative von Neumann regular rings exist in abundance. For example, all regular self-injective ... more Separative von Neumann regular rings exist in abundance. For example, all regular self-injective rings, unit regular rings, regular rings with a polynomial identity are separative. It remains open whether there exists a non-separative regular ring. In this note, we study a variety of conditions under which a von Neumann regular ring is separative. We show that a von Neumann regular ring R is separative under anyone of the following cases: (1) R is CS; (2) R is pseudo injective (auto-injective); (3) R satisfies the closure extension property: the essential closures in R of two isomorphic right ideals are themselves isomorphic. We also give another characterization of a regular perspective ring (Proposition 3.3)
We investigate the properties of periodic rings R in view of studying general skew polynomials . ... more We investigate the properties of periodic rings R in view of studying general skew polynomials . We introduce exponents for these polynomials and give some properties of this notion. We show, in particular, that this notion is right-left symmetric. Using the skew evaluation, we generalize the classical connection between the exponent of a polynomial and the order of its companion matrix.
We study the class of ADS rings and modules introduced by Fuchs. We give some connections between... more We study the class of ADS rings and modules introduced by Fuchs. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R is ADS as a right R-module must be either right self-injective or indecomposable as a right R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.
Leavitt path algebras of Cayley graphs arising from cyclic groups by G. Abrams and B. Schoonmaker... more Leavitt path algebras of Cayley graphs arising from cyclic groups by G. Abrams and B. Schoonmaker Characterizations of almost injective modules by A. Alahmadi, S. K. Jain, and S. Singh Automorphism-invariant modules by P. A. Guil Asensio and A. K. Srivastava Distributive algebras, isoclinism, and invariant probabilities by S. M. Buckley Ideals of the enveloping algebra $U(sl_3)$ by S. Catoiu On second submodules by S. Ceken and M. Alkan Open problems in coding theory by S. T. Dougherty, J.-L. Kim, and P. Sole Foundations of algebraic coding theory by S. T. Dougherty Counting $\mathbb{Z}_2\mathbb{Z}_4$-additive codes by S. T. Dougherty and E. Salturk From endomorphism rings to some noteworthy ideals in categories of modules by A. Facchini Lie and Jordan properties in group algebras by E. G. Goodaire and C. P. Milies Rad-projective $\delta$-covers by Y. Ibrahim and M. Yousif On lattices of annihilators by M. Jastrzebska and J. Krempa Clean elements in polynomial rings by P. Kanwar, A....
Separative von Neumann regular rings exist in abundance. For example, all regular self-injective ... more Separative von Neumann regular rings exist in abundance. For example, all regular self-injective rings, unit regular rings, regular rings with a polynomial identity are separative. It remains open whether there exists a non-separative regular ring. In this note, we study a variety of conditions under which a von Neumann regular ring is separative. We show that a von Neumann regular ring R is separative under anyone of the following cases: (1) R is CS; (2) R is pseudo injective (auto-injective); (3) R satisfies the closure extension property: the essential closures in R of two isomorphic right ideals are themselves isomorphic. We also give another characterization of a regular perspective ring (Proposition 3.3)
We investigate the properties of periodic rings R in view of studying general skew polynomials . ... more We investigate the properties of periodic rings R in view of studying general skew polynomials . We introduce exponents for these polynomials and give some properties of this notion. We show, in particular, that this notion is right-left symmetric. Using the skew evaluation, we generalize the classical connection between the exponent of a polynomial and the order of its companion matrix.
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Papers by André Leroy