article · Pacific Journal of Mathematics · 1987

Matrix rings over ∗-regular rings and pseudo-rank functions

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Abstract

In this paper we obtain a characterization of those * -regular rings whose matrix rings are *-regular satisfying LP ~ RP. This result allows us to obtain a structure theorem for the *-regular self-injective rings of type I which satisfy LP ~ RP matricially. Also, we are concerned with pseudo-rank functions and their corresponding metric completions. We show, amongst other things, that the LP ~ RP axiom extends from a unit-regular * -regular ring to its completion with respect to a pseudo-rank function. Finally, we show that the property LP ~ RP holds for some large classes of *-regular self-injective rings of type II.

Cite this paper

APA 7

Ara, P. (1987). Matrix rings over ∗-regular rings and pseudo-rank functions. Pacific Journal of Mathematics, 129(2), 209–241. https://doi.org/10.2140/pjm.1987.129.209

MLA 9

Ara, Pere. “Matrix rings over ∗-regular rings and pseudo-rank functions.” Pacific Journal of Mathematics, vol. 129, no. 2, 1987, pp. 209–41, https://doi.org/10.2140/pjm.1987.129.209.

Chicago

Ara, Pere. 1987. “Matrix rings over ∗-regular rings and pseudo-rank functions.” Pacific Journal of Mathematics 129 (2): 209–41. https://doi.org/10.2140/pjm.1987.129.209.

Harvard

Ara, P. (1987) ‘Matrix rings over ∗-regular rings and pseudo-rank functions’, Pacific Journal of Mathematics, 129(2), pp. 209–241. Available at: https://doi.org/10.2140/pjm.1987.129.209.

BibTeX

@article{ara1987matrix,
  title = {{Matrix rings over ∗-regular rings and pseudo-rank functions}},
  author = {Ara, Pere},
  journal = {Pacific Journal of Mathematics},
  volume = {129},
  number = {2},
  pages = {209--241},
  year = {1987},
  doi = {10.2140/pjm.1987.129.209}
}

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