# Sh:397

- Shelah, S. (1992).
*Factor = quotient, uncountable Boolean algebras, number of endomorphism and width*. Math. Japon.,**37**(2), 385–400. arXiv: math/9201250 MR: 1159041 -
Abstract:

We prove that assuming suitable cardinal arithmetic, if B is a Boolean algebra every homomorphic image of which is isomorphic to a factor, then B has locally small density. We also prove that for an (infinite) Boolean algebra B, the number of subalgebras is not smaller than the number of endomorphisms, and other related inequalities. Lastly we deal with the obtainment of the supremum of the cardinalities of sets of pairwise incomparable elements of a Boolean algebra. - No downloadable versions available.

Bib entry

@article{Sh:397, author = {Shelah, Saharon}, title = {{Factor = quotient, uncountable Boolean algebras, number of endomorphism and width}}, journal = {Math. Japon.}, fjournal = {Mathematica Japonica}, volume = {37}, number = {2}, year = {1992}, pages = {385--400}, issn = {0025-5513}, mrclass = {06E05 (03C05 03E35 03G05)}, mrnumber = {1159041}, mrreviewer = {Martin Weese}, note = {\href{https://arxiv.org/abs/math/9201250}{arXiv: math/9201250}}, arxiv_number = {math/9201250} }