top
We introduce the notions of T-Rickart and strongly T-Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that R is right Σ-t-extending if and only if every R-module is T-Rickart. Also, every free R-module is T-Rickart if and only if , where R’ is a hereditary right R-module. Examples illustrating the results are presented.
S. Ebrahimi Atani, M. Khoramdel, and S. Dolati Pish Hesari. "T-Rickart modules." Colloquium Mathematicae 128.1 (2012): 87-100. <http://eudml.org/doc/283848>.
@article{S2012, abstract = {We introduce the notions of T-Rickart and strongly T-Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that R is right Σ-t-extending if and only if every R-module is T-Rickart. Also, every free R-module is T-Rickart if and only if $R = Z₂(R_\{R\})⊕ R^\{\prime \}$, where R’ is a hereditary right R-module. Examples illustrating the results are presented.}, author = {S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pish Hesari}, journal = {Colloquium Mathematicae}, keywords = {t-extending modules; t-Baer modules; T-Rickart modules; strongly T-Rickart modules}, language = {eng}, number = {1}, pages = {87-100}, title = {T-Rickart modules}, url = {http://eudml.org/doc/283848}, volume = {128}, year = {2012}, }
TY - JOUR AU - S. Ebrahimi Atani AU - M. Khoramdel AU - S. Dolati Pish Hesari TI - T-Rickart modules JO - Colloquium Mathematicae PY - 2012 VL - 128 IS - 1 SP - 87 EP - 100 AB - We introduce the notions of T-Rickart and strongly T-Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that R is right Σ-t-extending if and only if every R-module is T-Rickart. Also, every free R-module is T-Rickart if and only if $R = Z₂(R_{R})⊕ R^{\prime }$, where R’ is a hereditary right R-module. Examples illustrating the results are presented. LA - eng KW - t-extending modules; t-Baer modules; T-Rickart modules; strongly T-Rickart modules UR - http://eudml.org/doc/283848 ER -